Ok, you asked if it would kill an elk, the answer is yes, but a .22lr will kill a mule deer too.

I' m also unsure of whether or not it would be legal at all, with proper handloads, if the rule is 550ft.lbs. @ 50yrds, a stong gun could stretch some power out to be JUST legal, but I don' t know how well your S&W will handle that? You might try loading up some that would be above regulation, but they' re going to be very hot, so BE CAREFULL!!! Plus, they' re going to buck like a son-of-a-gun, so you might consider that when you' re thinking about your hunt.

As far as .357 handguns go, the only thing better for elk than a 8 3/8" bbl is the 12" bbl, but that isn' t saying much, since neither is very good for it. Even if you were sure to be rather close, that' s still a lot of HARD muscle to go through for such a weak round (funny to say that about a .357). I' d say do yourself a favor and bump up to a .44mag at least, if not a Cassul (.454).