A semi-analytical fully discretised finite strip method is developed to investigate the pre-buckling and local buckling of viscoelastic plates with different boundary conditions subjected to time-dependent loading. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. The fully discretised finite strip equations are developed using a two point recurrence formulation which leads to a computationally superior formulation. Time history of maximum deflection of plates with different end conditions is calculated. The effect of unloading on of plates is evaluated. Moreover, a nonlinear approach is used to calculate the critical load of plates subjected to in-plane compressive loads. The effects of thickness, length of plate and transverse loading on critical buckling load are also studied. In addition, the finite strip method is developed using bubble functions. The displacement functions of plate are evaluated using a continuous harmonic function series that satisfies the boundary conditions in the longitudinal direction and a piecewise interpolation polynomial in the transverse direction. Finally, the first shear order theory of plates is used to evaluate the maximum deflection and critical load of viscoelastic moderately thick plates .
