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In this paper a damage model, with different damage surface in tension and compression, is formulated, implemented and validated to study elements of plain and reinforced concrete under actions which induce their collapse. For modelling reinforced concrete elements, the constitutive behaviour of concrete considers the softening deformation with a damage surface, whereas the hardening of the reinforcing steel is represented by a plasticity surface of Von Mises. Perfect bond between both materials was considered. The developed model does not exhibit the problem of stress locking as the smeared cracking model does; this guaranties an adequate energy release as the material fails. Numerical examples are presented showing the validity of the developed damage model for studying the behaviour of these elements up to their collapse.