A model is described for considering the partial slip that occurs when a pressurized crack intersects a joint to which it is perpendicular. The crack is assumed not to penetrate into the undamaged material; rather, opening of the crack occurs at the juncture through interfacial slip. Within the interfacial slip region, the resistance to slip is accounted for by prescribing the shear stress there. Results are obtained as the hydraulic loading in the crack is increased, and the subsequent crack growth is investigated. It is found that for a prescribed critical value of stress intensity factor the crack length remains fixed until a certain value of pressure is attained. Above this value the crack length can increase with increased pressure.