Abstract <p>The paper is concerned with derivation and application of basic equations of solid mechanics in the special coordinate frame in which the space and the time coordinate axes are not orthogonal. In this frame, the object velocity, in principle, cannot reach the velocity of light. The equations which generalize the classical Lorentz transformations in special relativity are obtained. They demonstrate that, in contrast to the classical theory, the length of the line element cannot become zero and the body mass cannot become infinitely high. As application, the general relativity spherically symmetric problem of gravitational collapse and expansion is considered. The external solution for an empty space and the internal solution for a pressure-free sphere are obtained in the proposed non-orthogonal coordinate frame.</p>