In an elastic crawler (10) and an elastic crawler drive mechanism (100), at least a portion of the outer edge of an engaging portion (12) has a cross-sectional arc shape such that both the trajectory drawn by the outer edge of the engaging portion (12) from when the engaging portion (12) starts to enter a tooth groove of a sprocket (20) until engagement between the engaging portion (12) and teeth (22) is complete and the trajectory drawn by the outer edge of the engaging portion (12) from when the engaging portion (12) starts to disengage from the teeth (22) until disengagement is complete do not project further outward than the outer edge of the engaging portion (12) when the engagement is complete.