Basalt-fiber-reinforced epoxy (BFRE) composite laminates fabricated using the vacuum infusion process were subjected to axial compression to assess their buckling behavior. The buckling responses of open-hole specimens were compared with those of plain ones. ABAQUS finite-element predictions of BFRE composite buckling agreed well with experimental results. A validated numerical model was used to perform a parametric investigation into the effects of open-hole specimen geometry and boundary conditions of specimens on their buckling behavior. A linear analysis was carried out to estimate the effect of geometric imperfections of specimens on their buckling. Also, glass-fiber-reinforced epoxy specimens were analyzed for their buckling response and compared with that of BFRE ones. The results of this study can be used for buckling-based designs of open-hole composite structures.