Modeling concrete fracture is important in order to uncover accurately the sources of distress which lead to the damage or failure of structures. Many different numerical approaches have been used in the past employing either a smeared or a discrete cracking approach. Those models have difficulty in capturing the local nature of cracking, as well as the direction of crack propagation. Lattice modeling and peridynamics (PD) are some of the more recent nonlocal fracture simulation tools which possess advantages, such as ease of modeling and accuracy of crack propagation simulations with few key parameters. In this work, we employ an overlapping lattice approach, where the continuum is discretized using truss elements extending over a predefined horizon similar to the concept used in PD with the sequentially linear analysis technique. Simulation results for several reinforced concrete (RC) and un-RC tests demonstrate the ability to estimate crack propagation directions and widths accurately, with the proposed modeling approach also offering a rather simple and intuitive approach.