The purpose of the study is the stability analysis of dynamic buckling behavior of mechanical systems subjected to multi-directional excitation wave. A Mathieu type in large elastic deformation model is proposed for the buckling where the coodinate transformations of load and displacement are taken into account. The analysis is carried out by numerical simulation with an elastic beam, where vertical and the rotational loads in sinnsoidal form are applied simultaneously. In comparing to a widly used buckling model,the simulation results show the proposed model leads to larger deformation.