This text is based on lectures given by the authors to students of the Physico Technical Institute in Moscow in the course of many years. Teaching mechan ics of continuous media to students in physics has some specific features. Un fortunately, the students rarely have enough time for this branch of science. Over a comparatively short period of time and without sophisticated mathe matics, the lecturer has to set forth the principal facts and methods of this rather important aspect of theoretical physics. The goal can be achieved only if the knowledge and intuition obtained by students in other courses has been mobilized efficiently. These observations have extensively been taken into account when classical as well as more contemporary and actively developing branches of mechanics of continua are considered. The theory of wave propagation is the most important topic in mechanics of continua for those who work in the field of physics and geophysics. That is why most attention is paid to this topic in the main text as well as in numerous exercises. The propagation of various kinds of hydrodynamic, magnetohydro dynamic, acoustic and seismic waves is considered in some detail. We begin with simple questions and proceed to more complicated ones. Accordingly, we treat the elasticity theory first. In the limits this appears to be simpler than the mechanics of fluids. For further study of each topic the reader will find references in the bibliography.