SummaryIn classic discontinuous deformation analysis (DDA), artificial springs must be employed to enforce the contact condition through the open‐close iteration. However, improper stiffness parameters might cause numerical problems. The main goal of this paper is to propose a new framework of DDA using second‐order cone programming. The complementarity relationship at contacts can be formulated directly; thus, artificial springs are avoided. Stemming from the equations of momentum conservation of each block, the governing equations of DDA can be cast as convex optimization problems. The basic variables in the formulations can be either block displacements or contact forces. The derived optimization problems can be reformulated into a standard second‐order cone programming program, which can be solved using standard efficient optimization solvers. The proposed approach is validated by a series of numerical examples.