This article deals with the optimal design of long and slender compressive struts. The main objective is to minimize the mass of the struts under certain non-failure constraints and thus find the optimal material. We show that the main failure mode of the struts is Euler buckling. The results clearly show that the struts should be constructed from unidirectional carbon fiber composites. A Monte-Carlo model for random microstructure homogenization of unidirectional composites is developed. We finish by performing a numerical computation of the effective properties of the chosen carbon fiber/epoxy composite using COMSOL MULTIPHYSICS software.