Add to ORKGThe objective of this paper is to present a computationally cost effective approach to limit and shakedown analysis of metal-matrix composite materials. The analyses presented are based on: the homogenization theory for periodic media, the kinematic limit and shakedown theorems and the finite element method in its displacement formulation. The resulting nonlinear mathematical programming problems are solved by an iterative procedure. The numerical tests performed so far exhibit fast convergence and show excellent agreement with numerical results arising from different approaches