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A numerical procedure is described for the elastic—plastic finite element analysis of crack propagation with branching. Constraint equations are used to model crack closing and sliding. Constraint conditions are imposed by using a penalty method for the self‐similar crack propagation and an elimination method for the off‐axis propagation. The contact condition is examined during plasticity iterations. The use of multiple constraints at the crack branching point to determine the mode of contact is discussed in detail. The method is then applied to (i) the self‐similar crack growth in a single‐edge notch specimen, (ii) the self‐similar propagation followed by interfacial splitting in a center‐cracked 0° composite plate, and (iii) the bifurcation of a crack in a compact tension specimen.