An algorithm is presented for sensitivity analysis of responses of an elastoplastic distributed parameter structure subjected to cyclic loading conditions. The structure is modeled by the finite element method, where an isoparametric element is used. The responses are found by using an explicit integration method incorporating higher-order differential coefficients with respect to the path parameter. All the governing equations are differentiated with respect to the design variables, and sensitivity coefficients of the responses are updated incrementally at each step. The accurate sensitivity coefficients are calculated for the value of the path parameter at the yield or unloading point. Since the algorithm is totally consistent with that of response analysis, the calculated sensitivity coefficients agree within good accuracy with those by the finite difference method.