Lattice models are well suited for crack simulations; however, their use has been mostly limited to the fracture of plain concrete. In this study, a practical two-dimensional mesoscale lattice composed of overlapping elements was employed to simulate the monotonic response of reinforced concrete elements. The force-deformation response of each element is calibrated from direct tension tests. An explicit time integration technique with novel proportional-integral-derivative control is used to efficiently simulate the response under monotonic loading. Six different reinforced concrete member simulations were conducted to validate the proposed approach. It was found that the proposed approach was capable of reproducing the load-deformation characteristics of elements failing in shear or flexure with a reasonable accuracy. A deterministic sensitivity analysis was conducted to uncover the response parameters with the most influence on the response estimations. Concrete tensile strength and steel yield strength were found to be the most influential parameters affecting strength and energy absorption capacities. Interestingly, the variation in fracture energy and tensile-softening parameters appeared to exhibit insignificant differences for strength and energy absorption estimations in the reinforced concrete simulations.