A three-dimensional theory of cross-ply laminated thick plates is developed via an elasticity approach for nonlinear impact modal analysis. The simply supported plate is strictly stress free over all four edges and both lateral surfaces, in addition to stress-loading equilibrium over the patch loading area. The 3-D dynamic displacement fields are expressed in a mixed mode of double Fourier series and cubic polynomials. A system of modified Lagrange’s equations is derived incorporating all surface conditions and interface displacement and stress continuities. Validity of the present 3-D theory is proved in comparison to the only existing exact solutions in the basic cases of statics and free vibration. The nonlinear impact modal analysis is performed using the Hertz contact law in patch loading and Green’s function for small time linearization. The 3-D displacements and stresses are found to predict a tensile crack at the unimpacted side and probably, a delamination at the interface. They are always unsymmetric with respect to the mid-plane in all cases of unidirectional, symmetric and antisymmetric cross-ply laminates due to the one-sided loading.