New energy conception of both solid’s fracture based on criteria of critical density of elastic energy, $p_{с}$, in fracture nuclei and three scale levels of the process, viz. atomic, microscopic and macroscopic ones, is developed in a given paper. Empirically observed regularity — the proportionality between increments of solid volume and potential energy of interatomic bonds at mechanical tension (in non-liner area of elastic deformations) and heating of solids—gives rise to these criteria. Parameter of density of interatomic-bond energy, $p_{0} = Q_{c}/V_{0}$ (where $Q_{c}$ is the sublimation energy, $V_{0}$ is the molar volume at 0 K), is a proportionality coefficient. This regularity is called as ‘the principle of constancy of density of potential energy within increment volume’ (PCDPE). On the basis of this principle, simple relations for calculation of a whole series of fundamental mechanical and thermal characteristics such as thermal-expansion coefficient, Young’s modulus, shear modulus, uniform (triaxial) compression modulus, sublimation energy, theoretical (ultimate) tearing and shearing strength, Grüneisen parameter, surface energy, etc. were obtained. All criteria of the critical density of energy include the constant $p_{0}$, and in specific case of material with atomically-sharp nanocracks, result in criterion similar to the Griffith’s one, but with a more precise (6 times greater) sufficient value of specific energy of the free-surface formation. It is shown that this new criterion is common for fracture in perfectly brittle solids as well as in quasi-brittle materials, and thereby substantially differs from classical Griffith’s criterion.