Abstarct: In this research, mathematical and numerical analysis of viscoelastic beams with moderately large deflection under transverse and axial load are presented. These equation are derived using the first order shear deformation theory. The kinematic of problem is according to the von- Karman strain-displacement relation and Hook's law is used as the constitutive equation. These equation are which a system of coupled nonlinear partial differential equation with constant coefficients have been derived by using Hamilton's principle. The governing equation have been solved analytically whit the perturbation technique and eigenfunction expansion method. 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, length, modulus of viscosity and elasticity on the system response, natural frequencies, buckling load. The results are compared whit the numerical method too.