The paper analyzes the tube extrusion process for work hardening materials by finite element limit analysis. Although limit analysis studies the asymptotic behavior of elastic-plastic materials, its concept can be extended to a class of work hardening materials. Finite element limit analysis based on a variational principle of duality consists of a 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 such as metal forming processes. Especially, the tube extrusion process for work hardening materials is simulated by the present algorithm as a demonstration of its validity and versatility.