Summary: The problem of an action on a cavity supported by a multilayer circular cylindrical shell located in the elastic half-space of a stationary moving load of an arbitrary profile is under consideration. The motion of the shell layers and the elastic half-space is described by the dynamic equations of the theory of elasticity in a moving coordinate system. Analytical solution of the problem of determining components of stress-strain state of the array and the shell at subsonic speeds of load movement at different contact interaction of the shells between each other and the array is obtained. Results of numerical calculations of stress-strain state of steel shell and surface of elastic mass at transport loads are given.