Brick masonry is one of the most widely used building materials worldwide, including in India. Globally, the strength and stiffness of clay brick vary from region to region. Most of the experimental and numerical analysis in the literature covers masonry with strong brick and weak mortar, where failure is characterized mainly at the brick–mortar interface. However, in certain instances, the locally available clay bricks can be weaker than the mortar used in the masonry construction. Therefore, this work aims to numerically simulate the weak brick and strong mortar masonry wall under in-plane shear loading. The discrete element method (DEM) framework is used for numerical simulation in 3DEC software. A simplified micro-modelling strategy is followed with smeared semi-rigid blocks and interfaces, considering the nonlinearities due to expected discontinuities in brick and brick–mortar interface. A coupled tension-shear and compression-shear contact constitutive model simulates the interaction between adjacent smeared brick–mortar blocks and within the smeared brick unit. The DEM framework is validated against the experimental observations available in the literature. The results indicate tensile failure at the interface, which can be attributed to a lower tensile strength of the brick unit and bond at the interface than shear strength. Further, a vertical crack pattern along the interface between smeared brick units and course detachment at the top and bottom corners is observed. The observed failure differs from the typically observed failure patterns in masonry with strong brick and weak mortar.