Laminate composites contain holes as a means of connection in industrial applications. A better understanding of the mechanical properties of open-hole components is necessary. Herein, progressive damage postbuckling analysis models are proposed for investigation of tensile damage and compressive buckling behaviors of open-hole laminate composites. The progressive damage model is based on failure criteria provided by the continuum damage mechanics model; virtual crack closure technology was employed to calculate the energy release rate for crack delamination in compressive postbuckling analysis. The models were utilized to analyze variations in the tensile and compressive mechanical properties, failure process, and buckling evolution of open-hole laminate composites using finite element analysis. The tensile failure patterns and failure processes of plies with different open-hole laminate composite angles were obtained and analyzed. Buckling characteristics, as well as the progression of buckling onset, buckling propagation, crack delamination, unstable delamination, and global buckling, were investigated. The influence of delamination crack length and crack distribution on the buckling properties of open-hole laminate composites are discussed in detail. Additionally, unstable and stable buckling characteristics were examined. The numerical results were in good agreement with theoretical and experimental results; damage initiated at the edge of a hole propagated to two sides with the onset of matrix damage, followed by fiber damage. The fiber damage of a 0°-ply led ultimately to laminate failure. The laminate with a symmetrical crack distribution showed stable buckling, whereas a short, nonsymmetrical distribution of cracks usually led to unstable buckling and delamination.