In the paper the influence of flexible covering properties on the linear development of disturbances in a supersonic boundary layer is investigated for Mach numbers M = 1.0, 2.0, 5.3, 6.0. As a model of a covering the porous plate closed by a flexible film is used. In the absence of gas in pores it is established that the flexible covering stabilizes boundary layer in the area of large Reynolds numbers and destabilizes it at small Reynolds numbers. Joint influence of the thickness and tension of a film leads to an appearance of additional unstable waves. For filled with gas pores the researches are conducted as taking into account losses of energy of disturbances in pores and in their absence. Calculations without power losses indicate possibility of existence of an absolute instability of the boundary layer on the flexible surface. The damping properties of a flexible covering connected with power losses in pores reduce their stabilizing role.