The permeability and coupled behavior of pore pressure and deformations play an important role in hydraulic fracturing (HF) modeling. In this work, a poroelastic displacement discontinuity method is used to study the permeability effect on the HF development in various formation permeabilities. The numerical method is verified by the existing analytical and experimental data. Then the propagation of a hydraulic fracture in a formation with a range of permeabilities is studied. The time required for propagation of an HF to 10 times its initial length is used to compare the propagation velocity in the formations with different permeabilities. The results obtained show that the HF propagation can be significantly delayed by a permeability less than almost 10-9 D. Also the effect of HF spacing on the propagation path is studied. It was shown that the stress shadowing effect of HFs remained for a longer spacing than in the elastic model due to the required time for fluid leak-off in the formation. Also the propagation angles are higher in the poroelastic model predictions than the elastic model. Therefore, it is proposed to use the poroelastic model when studying multi-HF propagation in order to avoid errors caused by neglecting the pore fluid effects on the HF propagation paths.