The standard explanation is that the Shonkin Sag was created by the catastrophic drainage of a huge periglacial lake, dammed up during the ice ages by the great ice sheets.  At some time the glaciers advanced to foot of the Highwood Mountains, thereby blocking the Missouri and other rivers flowing into the lake from the southwest.  When the ice began to melt, Lake Great Falls rapidly rose to a point where it could spill over the ridge at at the foot of the glacier.  The flow quickly eroded part of the glacier, and in one great swoosh cut a drainage channel toward the east. 

Undoubtedly parts of that story are plausible, and probably account for some chapters in the history of the Shonkin Sag.  There is much evidence for the existence of Lake Great Falls, including at least two shorelines at elevations of 3500 – 3600 ft (1067 – 1097 m) and 3800 – 3900 ft (1158 – 1189 m).  These shorelines are consistent with two spillway channels, A-B, and F-G.  Apparently F-G corresponds to an early episode, and the westward extension of that channel can be faintly traced on the slope above A-B.  The "gigantic spillway" picture is consistent with the formation of sections A-B, B-C, and F-G; but there are several problems in accounting for the remainder of the Sag:

• The change in gradient at point C
  Imagine the water, loaded with boulders and huge chunks of ice roaring down the steep slope B-C.  Why should it have suddenly slowed, and flowed along the nearly level channel beyond C?  Rivers just don't do that.  We should expect a big hole at C, or at least some evidence that the water was moving very fast and came upon a place where it was suddenly forced to change its velocity.
  
  
• The drainage divide beyond C
  Moreover, the actual principal local drainage divide is not pierced by A-B, but lies just to the east of C.  There is a long ridge - named Frenchman's Ridge - running from the mountains northward to the present canyon of the Missouri.  The ridge is at least partly made up of hard rock, for it forms the upper rim of the dry falls.  In pre-glacial times that ridge may have been slighly higher than the ridge at A-B.  It is punctured only by the Sag.  It is difficult to imagine how that ridge could have been breeched in a catastrophic flood unless there were already a pre-existing channel there.
  
  
• The low gradient over much of the length of the Sag
  The floor of the Sag is nearly flat for more than 34 miles, from the Junction with Shonkin Creek to the point where it joins the pre-existing valley of Flat Creek.  The elevation differences over that distance are less than 200 feet, which can easily be accounted for by erosion and filling by sediments washed down from the mountains over the past 10,000 years.  Such a negligeable gradient is common for mature valleys with meandering rivers, but unlikely for an overflow channel formed by a catastrophic flood.  If the Shonkin Sag were formed one catastrophic event we might expect the gradient to be rather irregular, with many ledges where the rapids formed as the water flowed over relatively resistant rock.  It seems more more likely that the Sag below point C was originally formed by a more leisurely flow acting over a long time.
  
  One complication that must be taken into account is the possibility of differential settling and uplift.  However the Highwood Mountains are the worn down remains of a massive intrusion several million years ago; and there are no active faults in the vicinity.  The igneous activity was finished millions of years ago.  If there is any vertical motion it is slow isostatic rebound, due to the erosion of much of the material in the center of the mountains.  This might be sufficient to account for variations of tens of feet; but it could not explain the low gradient of the Sag.
  
  
• The size and shape of the channels
  Further evidence suggesting that the picture is more complex than a single overflow event comes from the shape of the channel.
  
  The first diagram below shows the profile of the present valley of the Missouri River, sampled a short distance to the west at several points between the Falls of the Missouri and the town of Fort Benton.  The scale at the side indicates elevations in feet above sea level.  The vertical scale is magnified by a factor of 15, so each trace indicates a cross section 2 miles across.  This channel has presumably been excavated since the ice sheets decayed, over a period of 10,000 – 12000 years.  The profiles are very impressive, and are indicative of a relatively young valley excavated by a vigorous river.  The most important aspect to notice here is that the channel shape is relatively constant along this segment of the river valley.
  
  Keep in mind also that below the resistant ledge of hard rock which forms the Great Falls of the Missouri, the river is flowing through mainly shales and sandstones and a mixure of poorly consolidated crud.
  Now look at the profiles of the Shonkin Sag.  The locations of the profiles are indicated by thin orange lines on the map above.  Below the overflow channel, A-B, this is an rather abnormal valley.  If the valley were excavated by a single stream, with no significant tributaries entering from the sides, we might expect the power of the stream to diminish downstream.  But the channel actually becomes broader and deeper.  The lower part of the Shonkin Sag suggests that rather than a short lived catastrophic event, this was excated over a very long period.  Moreover, comparison with the Missouri channel, which was cut into much softer rocks, suggests that the total amount of water that flowed through the Sag may have been much greater than the amount that has flowed along the Missouri in the past 12,000 years!
  
  
• The sinuous channel along the lower part of the Sag
  The overflow is presumed to have been constrained by ice, which enveloped the north side of the Highwood Mountains, and caused the overflow to find a winding way between the ice and the mountains.  But a stream powerful enough to break through a rocky ridge would have been powerful enough to break up some of the ice blocking its way.  One might expect a catastrophic flood, like that which resulted fromt the overflow of Lake Missoula, spreading over a broad expanse at the food of the Highwood Mountains, carrying away ice, boulders, and everything in its path.

A more complete explanation for the Shonkin Sag is that it was formed over immensely long periods of glaciation, probably during at least several Ice Ages.  It was formed not by a single violent event, but in a much more complex sequence of events, including diversion of the flow of the Missouri river for most of the duration of the Ice Ages.  For the past million years the Earth has spent most of the time locked in ice; so there was sufficient time for a river to cut a channel around the ice—a channel that could have been scoured and enlarged by several violent overflow events.

Rather than a temporary, short-lived channel, the Shonkin Sag may have been the preferred channel for the Missouri River for immensely long times.  That it looks so fresh today, unlike the other valleys of the Missouri, is because it was never eroded by glaciers.

The composition of the rocks of the Highwood Mountains is very important to the creation of the Shonkin Sag.  Three minor mountain ranges in north-central Montana were formed as massive intrusions of relatively rare Shonkinite.  First were the Bears Paw Mountains, then the Highwood Mountains, and finally the Adel Mountains.  The presence of Shonkinite is thought to be related to the occurence of these volcanic intrusions far from a plate boundary or known hot spot.  Shonkinite is similar to Basalt, except that it is anomalously rich in Potassium.  Basalt is usually found near plate boundaries, hot spots, or fissure eruptions. 

The Shonkinite mountains were formed several million years ago, largely through the intrusion of laccoliths.  They probably looked rather like the more recent laccolithic Henry Mountains of eastern Utah.  They have been worn down rather quickly, so that the rock exposures are mostly just isolated ridges protruding from hills of rubble.  Shonkinite is generally black, but weathers quickly to a dark red.  A feature that may have been critical to the formation of the Shonkin Sag is that Shonkinite is often extremely friable; it can sometimes be broken in the hand.  Almost any impact, whether by ice, running water, or suspended boulders, can readily break off fragments from the exposed vertical faces.

The alternate model for the formation of the Shonkin Sag involves several distinct steps: