In this study, a numerical approach using irregular lattice model is developed to simulate failure behavior of reinforcement concrete(RC) at high strain rates of loading. In the irregular lattice model, the material domain is discretized by the Delaunay/Voronoi dual tessellation with their lattice connectivity of spring sets. Generally, cementitious materials have rate dependency on their mechanical properties with different rates of loading. During the numerical analysis, in order to achieve this material characteristic, a rheological unit with a combination of springs and dashpots is introduced into the rigid-body-spring elements of the lattice model. The material response in every time step is obtained based on the time integration scheme. To model the reinforcement within the matrix, a semi-discrete typed approach is adopted into the lattice model, in which the stiffness of a reinforcement is transformed into a corresponding spring set of concrete element.