The problems of wellbore stability are usually connected with the presence of weakness planes in the formation of rock. In this work we researched instability of borehole using the Nova and Zaninetti criterion on the base of results of Brazilian tests performed on two types of shale. We investigated in the wellbore stability mechanisms and mechanical properties of shales, which are represented through laboratory tests such as Uniaxial Compression Tests, Triaxial tests and Tensile tests. We used the results of the Brazilian tests, interpreted them with the Nova and Zaninetti criterion, and defined tensile strength parameters. We needed to verify that high mud pressures could cause the occurrence of tensile failure, so we calculated the mud pressures to avoid slip and tensile failure or fracturing pressure to avoid fractures for all the inclinations δ of the weakness planes.