Discussion covess dynamic response problem of an elastic plate with arbitrary boundary shapes on a half-space linear viscoelastic Winkler foundation impacted by a moving body.Undes the condition of a known initial velocity of the body, a non-linear Volterra integral equation on impact force F(t) is deduced, and the dynamic transverse deflection W(x,y,t) of the plate is put forward. To solve the integral equation, an effective numerical computation method is used. At the end, results of two practical examples are shown and discussed.