The causes of the nonlinear behavior of concrete until failure are numerous and complex, particularly for nonmonotonic and rapid loadings. A model is presented coupling damage and plasticity including several effects: Development and closure of cracks, damping, compaction, and strain rate effects. The idea is to describe, with the same tools, a wide variety of problems, the model is of explicit form, and what makes possible its implementation into explicit numerical scheme well adapted to the treatment of fast dynamic problems. In this context, the finite element "Abaqus explicit" code is used, and the model has been successfully applied during the past few years to model a large range of complex reinforced concrete structures subjected to severe loadings. In this paper, the main model concepts are presented, and some examples of numerical simulations are given and compared with experimental data. The applications proposed are related to quasi-static loading as well as to rapid loading (impact); In particular, one of them is within the framework of an experiment linked to the design of a reinforced concrete rock-shed gallery located in the French Alps. The results show the relevance of the modelling used, which makes some real numerical experiments very useful for complex structures and/or extreme loadings.