**Sotion of Mixed Dynamic Boundary Problem for
Elastic Halfspace.**

The problem of motion of isotrop elastic halfspace on plane boundary of which along halfplane x ³ 0 are given horizontal displacements, and on x £ 0 halfplane shear stressare are equal to zero. Solution is obtained by integral transforms method and is brought to Wiener-Hopf system, which is solved by circulants method and by solution of Fredholm integral system.