Abstarct: In this research, mathematical and numerical analysis of beams with moderately large deflection under transverse and axial load are presented. These equations are derived using the first order shear deformation theory. The kinematic of problem is according to the von karman strain-displacement relation and the Hook's law is used as the constitutive equation. These equations which are a system of coupled nonlinear partial differential equations with constant coefficients have been derived by using the Hamilton’s principle. The matched asymptotic expansion method (MAE) and the Laplace transform has been applied to obtain the equations in Laplace domain. These displacements have been transmitted to the time domain by using the residual theorem. baxsed on this analytical solution, the response of the system, the buckling load and the natural frequencies, are determined for a given set of initial values. Finally, a parametric study is performed to investigate the effects of the various parameters such as thickness, density and length on the system response, natural frequency and buckling load. The results are compared with the numerical method too.