We study granular materials characterized by the possibility of interlocking between the particles. The Interlocking is modeled as the combined effect of sliding and rolling resistance at the contacts, and it involves two contact parameters: a coefficient of sliding friction and a coefficient of rolling friction. This model is introduced within the framework of the Contact Dynamics method, and it is applied to investigate the effect of the two contact friction coefficients on the behavior of large polydisperse granular samples sheared in a numerical simple shear device. The macroscopic behavior of the samples is investigated in terms of the steady‐state shear strength and the fabric properties of the packing. We find that two regimes can be distinguished in which the steady‐state shear strength is controlled by either sliding friction or rolling friction. Moreover, our results show that the introduction of rolling friction strongly affects the microstructure of the packing. In particular, with high values of the sliding and rolling friction coefficients, the force‐carrying backbone takes an increasingly columnar aspect involving a weak proportion of particles and affecting the mechanical role played by the weak network.