An analytical method that exactly satisfies the equations of the boundary-value problem for the inelastic response of laminated metal matrix composite tubes on a point-wise basis is presented. Because of the lack of a generally accepted constitutive relation for the inelastic behavior of metal matrix composites, the micromechanics relations known as "the method of cells" are used to compute the effective elastic composite behavior as well as the incremental inelastic response of the individual plies. The method of successive elastic approximations is then used in an iterative process to obtain the effective plastic strain distributions in the individual layers of the laminated tube. The model can be subjected to a variety of thermomechanical loadings. In addition to a classical incremental plasticity theory, a viscoplastic model is included in the analysis to simulate the time-dependent effects of a composite tube under load. The developed analytical scheme is subsequently incorporated into an optimization algorithm, resulting in a design tool for the optimization of arbitrarily layered metal matrix composite tubes in the presence of inelastic effects. Representative tubes are optimized with respect to a user-defined objective function by varying ply thickness and orientation, as well as the laminate's fiber volume fraction.