A technique for determining the stress-strain state of an elastic half-plane under a nonstationary load applied to its boundary is developed. The corresponding boundary-value problem with initial conditions is formulated. Laplace and Fourier transforms are used. The inversion of the joint transform enables obtaining the exact analytical expressions for the stress and displacement as functions of time and the distance to the boundary for some types of loads Keywords: elastic plane problem, nonstationary process, stress-strain state, Laplace transform, Fourier transform, Cagniard techniqueIntroduction. The nonstationary problem of elasticity has a long history and has intensively been developed due to practical importance, specific features of the physical processes, and interesting aspects of solving the corresponding boundary-value problems. Particular attention is usually given to problems for half-spaces (axisymmetric problem) or half-planes (plane problem) that are most often subject to a shock load or a normal stress suddenly applied to the boundary. The major results achieved in this field can be found in [3,6,13]. Some approaches and features of studies are described in [8-10, 12, 14-17].We will find the analytic solution to the nonstationary plane problem of elasticity for a half-plane under a distributed nonstationary load (normal stress) suddenly applied to its surface. The general solution of the problem will be found using the Laplace and Fourier transforms. The transforms will be jointly inverted using the Cagniard technique [9]. Doing so will lead to the exact analytic expression for the normal stress on the axis of symmetry of the problem as a function of time and depth for two types of load (stress linearly or parabolically distributed over the half-plane surface).1. Let us address the plane problem for an elastic half-space under a nonstationary load applied to its surface. We introduce Cartesian coordinates x y z , , such that the wave process occurs in the half-plane xz, the x-axis is directed along the boundary of the half-plane, and the z-axis is directed deep into it (Fig. 1).It is assumed that the normal stress symmetric about the z-axis is induced at some initial time t = 0 and, in the general case, is a function of time and the coordinate x.We introduce the following dimensionless notation: