The paper deals with the plane unsteady problem of the collision of two rigid undeformable and shallow surfaces, one of which is covered by a thin layer of an ideal incompressible liquid. At the initial instant of time, a dry surface touches the liquid free boundary at a single point and then starts to penetrate the liquid layer. The flow region is divided into four parts: the region beneath the entering surface, the jet root, the spray jet and outer region. Inside each of those subdomains the flow patterns have their own peculiarities and are analysed separately. The matching conditions allow us to obtain the uniformly valid asymptotic solution of the original problem. The relative body motion and the characteristics of the spray jets generated under the impact are determined. The condition on the shapes of the bodies, under which the velocity of the impact of the rigid surfaces is non-zero, is derived.