The underlying factor that leads the wellbore collapse is the porepressure transient process of elevation around the wellbore due to the penetration of the drilling mud. Among the rock properties, the permeability is responsible for determining penetration speed, as well as the reached depth. When drilling shales, wich are rocks of low permeability, a zone of mechanical damage is developed around of the wellbore. This zone is characterized by the alteration of the mechanical and hydraulic rock properties. There is a material volume increase, accompanied by microcracking, as a result of the unloading and subsequent deviatoric stresses. This behavior of the material was represented in this work by a model of non-associated plasticity. Here is discussed the stresses and excavation influence on rock permeability, by testing the application of two permeability relationships to drilling problem. These relationships were implemented in a numeric simulator finite element based, wich can model the coupled process of the single-phase flow through porous media.The obtained results show that the consideration of constant permeability on zone close to the wellbore as constant, during and after the drilling, is a simplification that can lead to significant mistakes. The permeability relationships adopted, although still need experimental or field validation, will contribute to a best understanding of the study of the wellbores stability.