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The paper describes numerical simulations with a meso-scale discrete model, specifically the Lattice Discrete Particle Model (LDPM). The Voronoi tessellation is used to build the random geometry of the model. The previous solver was capable to simulate only static behavior of the concrete, development of the dynamic solver is the contribution of the present work. The simulation of the dynamic response is based on the implicit generalized-alpha method. A mass matrix involving translational and rotational inertia as well as eccentricity of the centroid of the particle is derived. Numerical examples of the simple cantilever beam loaded by single force at the free end are used to verify the transient response of the linear elastic material, in our case the plain concrete. Computed results with different model settings are compared with the analytical solution and static response. [ABSTRACT FROM AUTHOR]