Approximate solutions are given for the nonlinear bending response of thin plates of rectangular and circular geometry subjected to various boundary conditions such as simply supported and clamped-in edges. The investigation of the response of the plates has been restricted to two particular pulses, the step function and the exponentially decaying pulse, of which the latter can be used for an adequate description of a blast load on the plate. Proper transformation of the dependent time function, such that the additional transforming function will be a solution of the linear system disturbed by the same pulse function, will bring the time differential equation into a form so that Lighthill’s extension of Poincare´’s perturbation method can be employed for the solution of the problem.