A shock absorber for a washing machine and a washing machine having the same are disclosed. The shock absorber includes: a shock absorber sleeve, and the shock absorber sleeve defines an accommodation cavity therein; a shock absorber rod, movably connected to the shock absorber sleeve; an elastic member provided on the shock absorber rod and/or the shock absorber sleeve; a first damping member fitted over the shock absorber rod and mounted on the shock absorber sleeve; and a second damping member mounted on the shock absorber rod and accommodated in the accommodation cavity. The first damping member and the second damping member generate damping when the shock absorber rod moves relative to the shock absorber sleeve. The shock absorber for the washing machine has a simple structure and favorable shock absorbing effects, and occupies little space.