I have used SST's in a couple of Handi-Rifles:

95 grainers in a .243 to kill a doe antelope at about 200 yards; broke the off-side shouler and exited. I was kind of impressed...not much meat damage really;
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then a 117 grainer in a 25 Remington to kill a doe mule deer at about 70 yards. No major bones were struck,the bullet exited. Again, I was satisfied with its performance.

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Velocities were moderate, neither load would be considered maximum. However, elk are big, tough animals. One would have to really be careful of the shot agle, trying to place a bullet in the vitals without hitting any large bones with SST's, I think.