The current theory of the strength of solids is supplemented by an account of thermodynamic linear tension and its variations in the course of crack growth. For the case of dispersion interactions, two mechanisms of crack growth are compared, i.e., the conformal mechanism (when the angle at the crack tip is conserved) and the depth mechanism (when the width of crack mouth is conserved); it is shown that the second mechanism is more energy favorable. For both mechanisms, as well as for the case of constant linear tension, relations for the ultimate strength are derived, irrespective of the type of interactions, which clarify known Griffith and Sack criteria for linear and disc-like cracks, respectively. It is established that the role of linear tension in similar criteria increases with the narrowing of the crack and becomes significant in nanocracks. It is shown that an increase of linear tension upon the introduction of sorbate into the crack does not interfere with the effect of adsorption-induced reduction of strength (the Rehbinder effect).