A vast number of numerical approaches have been used to simulate the non-linear behaviour of concrete and reinforced concrete members at different scales. Most approaches were based on the finite-element method and have a variety of disadvantages when modelling brittle materials. Thanks to increasing computational power, mesoscale lattice models have been developed to achieve more accurate results for the width and pattern of cracks. Among different element choices for the lattice network, the use of truss elements is more efficient than beam or shear elements. In this study, a two-dimensional mesoscale lattice model is proposed with the novelty of grid perturbation to enable the prediction of compression failure as a consequence of tension failure. A novel calibration technique is proposed to determine the magnitude of grid perturbation. Uniaxial compression simulations to investigate the relationship between tensile and compressive strengths are described. The length scale and grid dependency of the model are investigated numerically. In addition, compression strut experiments and overreinforced concrete beam tests are simulated to validate the proposed approach. Promising numerical results show that compression failure can be estimated using lattice models that have tension failure only.