This research deals with the oblique impact contact of a simply supported laminated plate by a rigid impactor, in which the moving boundary problem is composed of an undetermined contact area and undetermined contact stresses distribution with anisotropic friction. By using the three-dimensional theory of laminated plates and shells, an innovative solution method is introduced for the governing equations of contact stresses via the energy variation and contact mechanics approach. Volumetric displacements and discrete patch loadings are considered as control variables and state variables, respectively. Three-dimensional boundary conditions with contact surface anisotropic friction, interlaminar continuity of layer displacements, and transverse stresses are included. Impact responses are acquired through modal superposition in terms of the loading distribution rather than conventional displacement fields. Using small incremental linearization, the non-linear oblique impact contact problem (involving discrete pressures and the final contact area) is solved by iteration. Three-dimensional dynamic displacements and stresses can be evaluated throughout the laminated plate.