The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The elastic potential is given in general form and is only specified for numerical purposes. The dependence of the critical velocity of the load and the stress-strain state on the prestresses is analyzed for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations are carried out for a half-space with Bartenev-Khazanovich potential Keywords: initial stresses, load moving with constant velocity, two-layer half-space, incompressible material, Bartenev-Khazanovich potentialIntroduction. Three-dimensional linearized theories of stability of deformable bodies and elastic waves in prestressed bodies were analyzed from a contemporary standpoint in [7,8], respectively. The results of [7,8] were used in modern analysis of inverse problems for elastic waves in prestressed bodies in [19], contact interaction of elastic prestressed bodies in [5,6], stability of mine workings in the case of an inhomogeneous subcritical state in [9], and exact solutions of mixed plane problems in the case of prestresses in [18]. The motion of cracks in elastic prestressed bodies was studied in [10-13] for homogeneous bodies and in [14][15][16][17] for piecewise-homogeneous bodies. Static contact problems for elastic bodies were solved with and without regard to prestresses in [20-22, 24, etc.].The present paper addresses a plane problem for a plate subject to a concentrated mechanical load and lying on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is incompressible and isotropic in the natural state. The elastic potential has a general form, which will be specified for numerical purposes. We will analyze the dependence of the critical velocity of the load and the stress-strain state on the prestresses for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations will be conducted for a half-space with Bartenev-Khazanovich potential.1. Consider a plate of thickness 2h on an elastic half-space whose initial strain state is determined by the following components of the generalized stress tensor:

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