The present invention provides a shock absorber with compliant members. Shock absorption is provided by the bending and rebound of curved, flexible arms. The deflection and the damping capabilities of the shock absorber are determined by the dimensions, curvature, and material modulus of elasticity of these compliant members. The shock absorber with compliant members technology may be applied to a bicycle front fork shock absorber and a rear shock absorber, both described herein. The benefits of a shock absorber with compliant members are that it is light-weight, it is simple in design, it has few movable joints, it can be designed to have precise flexion and damping characteristics, and it is resilient in harsh conditions.