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The paper analyzes the extrusion process of work hardening materials by the finite element limit analysis. Although limit analysis studies the asymptotic behavior of elastic-plastic materials, its concept can be extended to the class of work hardening materials. The finite element limit analysis based on a variational principle of duality consists of limit formulation, finite dimensional approximation, and a minimization technique. Since the finite element limit analysis guarantees stable convergence and computational efficiency, it is suitable to a class of nonlinear solid mechanics problem like metal forming process. Especially, the extrusion process of work hardening materials is simulated by the present algorithm as a demonstration of its validity and versatility.