<p>Using the three-dimensional linearized theory of stability and piecewise-homogeneous medium model, this study has investigated near-surface buckling in the laminated composite materials, as well as local buckling in the vicinity of interlayer macrocracks. The effects of macrocrack size and position on critical loads and buckling modes have been thoroughly analyzed. It has been demonstrated that, as the macrocrack size increases reaching a certain value, the near-surface buckling mode abruptly changes over to local buckling. To solve the problem numerically, a mesh-based method and a modified variational-difference approach have been applied. A computational experiment has been conducted using both sequential and parallel implementations of the Cholesky method to solve the resulting system of linear algebraic equations, as well as the subspace iteration method to solve the generalized eigenvalue problem.</p>