Taking into account the current value of the coefficient of lateral deformation the rheological relation describing the nonlinear elastic behavior of compressible medium is introduced. The energy consumption for the specimen with crack made of considered material is calculated and the fracture criterion is formulated. In particular, for the brittle material, when the coefficient of lateral deformation is equal to zero, the received criterion is identical with the Griffith’s fracture law. In the general case, the criterion is dependent on the coefficient of lateral deformation. Similar to the Griffith’s criterion, the critical value of crack length from the critical value of stress is governed by the hyperbolic law.