Experiments to study the behavior of various materials point to the relation that exists between elastic properties and the type of stress. The influence of the state of stress on the elasticity of a fractured material will be discussed for a physically non-linear model of an elastic solid. The strain-dependent moduli model of material, presented in this paper, makes it possible to describe this feature of a solid. It also permits to simulate a dilatancy of rocks. A damage parameter, introduced into the model using a thermodynamical approach, allows to describe a rheological transition from the ductile regime to the brittle one, and to simulate the rock's memory, narrow fracture zone creation and strain rate localization. Additionally, the model enables the investigation of the final geometry of fracture zones, and also to simulate their creation process, taking into account pre-existing fracture zones. The process of narrow fracture zone creation and strain rate localization was simulated numerically for single axis compression and shear flow.