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The three-dimensional linearized theory of stability and a piecewise-homogeneous material model are used to determine numerically the stability-critical parameters of a laminated composite with compressed reinforcement plies. Mixed boundary conditions (regular material structure and symmetric surface loading) on the sides of a composite specimen and boundary conditions for stresses on one side that is free of stresses are analyzed. It is established that the critical load depends on the ratio of the geometrical and mechanical characteristics of the composite components and the composite specimen as a whole. The effect of the inhomogeneity of the initial state due to the surface loading on the buckling modes is studied. It is shown that the composite undergoes microbuckling near the loaded surface with buckling modes damped with distance from the end, which is the end-crushing failure mechanism in composites [ABSTRACT FROM AUTHOR]