The failure behavior of concrete structures is simulated using a random lattice model, in which the rate dependent features are described by a visco-plastic damage model. Steel reinforcement is explicitly incorporated within the model without introducing additional degrees of freedom to the system. As part of a calibration process, direct tensile tests are simulated at various strain rates. Validation efforts are made through simulations of four-point bending tests of RC beams under different loading rates. Finally, the enhancement of dynamic failure resistance by various reinforcement conditions is investigated through the simulations of four-point bending tests under a higher loading rate.