Thin plate structures are more widely used in many engineering applications as one of the structural members. Generally, buckling strength of thin shell structures is the ultimate load carrying capacity of these structures. The presence of cracks in a thin shell structure can considerably affect its load carrying capacity. Hence, in this work, static buckling strength of a thin square plate with a centre or edge crack under axial compression has been studied using general purpose Finite Element Analysis software ANSYS. Sensitivity of static buckling load of a plate with a centre or a edge crack for crack length variation and its vertical and horizontal orientations have been investigated. Eigen buckling analysis is used to determine the static buckling strength of perfect and cracked thin plates. First, bifurcation buckling loads of a perfect thin plate with its mode shapes from FE eigen buckling analysis are compared with analytical solution for validating the FE models. From the analysis of the cracked thin plates, it is found that vertical cracks are more dominant than horizontal cracks in reducing buckling strength of the thin plates. Further, it is also found that as the crack length increases, buckling strength decreases.