In this work, a nonlocal damage-plasticity model for dynamic finite element analyses of cohesive structural elements is presented. The proposed cohesive model is able to reproduce the main relevant behaviors of quasi-brittle materials despite being quite simple, i.e. governed by only a few parameters which can be determined by standard laboratory tests. In particular, the model is able to reproduce the mechanisms of cohesive materials under static or dynamic loads: degradation of the mechanical properties (damage) and accumulation of irreversible strains (plasticity). Moreover, the model also simulates the cyclic macroscopic behavior of quasi-brittle materials, taking into account the loss and recovery of stiffness due to crack closure and reopening. The latter effect represents a particularly important characteristic in the case of dynamic loads. The proposed formulation is implemented as a constitutive model for two-dimensional plane stress four-node quadrilateral elements. The second order equations of motion are solved adopting the implicit Newmark time integration scheme. The proposed model is validated and its dynamic performance is numerically demonstrated through the analysis of a large-scale structural element.