Abstract The subject of this paper is the application of basic ideas and methods of continuum mechanics to the crack propagation processes. The crack extension is governed by an additional condition at the crack-tip. As a consequence of this a problem of “fine” structure of the crack-tip is considered. The general additional condition for any model of continuum is obtained making use of the energy conservation law and of the physical concept about the fracture energy. Dynamic cracks in elastic solids and quasi-static cracks in elastic- and rigid-plastic solids are briefly considered, as well as a problem of the crack extension in dissipating viscoelastic bodies. The general approach is also applied to the case of fatigue and “fluctuation” cracks.