This paper presents geometrically nonlinear transient analysis of rectilinearly orthotropic thin rectangular plates resting on Winkler and Pasternak foundations for uniformly distributed step function and sinusoidal pulse loadings. The orthogonal point collocation method in the space domain and Newmark-β scheme in the time domain are employed. Immovable clamped and simply-supported plates are analyzed. An approximate method is used to predict the maximum dynamic response to step loads from the results for static loads and is found to yield sufficiently accurate results. Some of the plates covered include glass-reinforced and boron-reinfored plates.