A numerical method is presented in this paper for determining the load–bearing capacities of ductile composites such as metal matrix composites based on homogenization theory and the kinematic limit theorem. A representative volume element is chosen to reflect the microstructure of a periodic composite. By directly introducing the von Mises yield criterion into the kinematic limit theorem, a nonlinear optimization formulation can be obtained to calculate the ultimate strength of a ductile composite. The finite–element modelling of the kinematic limit analysis is formulated as a nonlinear mathematical programming problem with equality–constraint conditions, which can be solved by a direct iterative algorithm. An interface failure model based on the microscopic fluctuation displacements is proposed to account for the effects of interfaces on the failure of composites. The present method can effectively reveal the effects of the microstructure on the macroscopic properties and micromechanical failure mechanisms of composites. Finally, some numerical examples illustrate the validity of the present method.