Actually, if one goes uphill and downhill at "constant velocity", the work done by the muscles is identical in both cases. You can verify this by stepping up a single stair "very slowly" with one leg, and then lowering yourself back down "very slowly". You've expended the same amount of energy (work) going up as coming down. The difference in running downhill is that you are more in "free fall" between steps and your joints absorb more of the force in decelerating than your muscles, so less work is done by your muscles. Professor Wilson from Marshall Physics Department.

Actually, if one goes uphill and downhill at "constant velocity", the work done by the muscles is identical in both cases. You can verify this by stepping up a single stair "very slowly" with one leg, and then lowering yourself back down "very slowly". You've expended the same amount of energy (work) going up as coming down. The difference in running downhill is that you are more in "free fall" between steps and your joints absorb more of the force in decelerating than your muscles, so less work is done by your muscles.