We use a 2D forward finite-element model to explore how a laterally continuous permeable bed impacts the geological evolution and the geomechanical properties of a salt basin. We show that a permeable bed tilted by rise of a salt diapir substantially increases pore pressure in sediments near the diapir through hydraulically connecting these sediments to deep, high-overpressure sediments far from the diapir. The pore-pressure increase near the diapir has the following significant consequences: it causes a faster rise of the diapir; brings sediments near the diapir close to shear failure in situ; causes unloading of sediments around the crest of the permeable bed; and reduces the margin of appropriate mud weights for drilling near the diapir. The rise of the salt diapir induces concentrated lateral deformation and thereby overpressure in mudrocks encasing the permeable bed in an area near the bottom of the basin. This anomalously high overpressure is in marked contrast with the overpressure in the permeable bed, resulting in a large pore-pressure gradient between the permeable bed and encasing mudrocks. Our study provides insight into the importance of permeable beds to the structural evolution of a salt basin and to the exploration and production of hydrocarbon near salt diapirs.