In this study, the linear and nonlinear displacement responses of an antisymmetric angle-ply composite plate subjected to sonic boom and air blast loadings are addressed. The first-order shear deformation theory is used for the governing equations so that the shear deformations can be taken into account for the responses of moderately thick plates. The von Karman type of geometric nonlinearities; are considered and the rectangular composite plate is assumed to be simply supported on all edges. A multimode Galerkin approach is used to obtain the equation of motion in the time domain, and those equations are solved by a Runge-Kutta fifth-order method. The influences of a large number of parameters are investigated, such as damping ratio, geometric nonlinearity, number of modes, characteristic of the blast, plate geometry, and fiber orientation.