AbstractA finite element approach for shape optimization in two‐dimensional (2‐D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary.The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B‐spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented‐Lagrangian techniques (to solve the contact problem) and an interior‐point mathematical‐programming algorithm (for shape optimization), we obtain several results reported at the end of the article.