Design sensitivity analysis of structural problems obeying an elastoplastic material behavior is developed using adjoint variable method. An elastoplastic constitutive equation with yield surface and kinematic hardening is considered to describe the material behavior. The traditional incremental procedure and its design variation need special treatments in order to predict the discontinuity of the structural response sensitivity because the contribution from the design sensitivity at the material transition point is lost during the calculation. In this study, discontinuities of the design variations at the material transition points are alleviated in the adjoint variable method. Analytical and numerical examples are used not only to demonstrate the developed sensitivity procedure but also to gain insights of numerical implementation for the design sensitivity analysis of the elastoplastic structure based on the adjoint variable method. The comparisons between adjoint variable and direct variation methods are also discussed.