A general boundary element methodology for the dynamic analysis of 2-D and 3-D solids and structures exhibiting quasi-brittle material behavior is presented. Inelasticity is modeled with the aid of the elastic damage theory. Strain rate and cyclic loading effects are also considered. The integral formulation of the problem employs the electrostatic fundamental solution and thus both surface and volume integrals due to inertia and inelasticity are created. Consequently the discrimination involves both the surface and the interior of the body. The singular integrals are evaluated by advanced numerical integration techniques, while Humboldt's step-by-step time integration scheme is used to obtain the dynamic response. Numerical examples are presented to illustrate the proposed method and demonstrate its accuracy and potential.