With the present state of development of computer programs, inadequate material models are often one of the major factors in limiting the capability of structural analysis. This is especially true for concrete where generally accepted constitutive equations do not exist. Nevertheless, there exists a large variety of models which have been proposed in recent years to characterize the stress-strain and failure behavior of concrete materials. All these models have certain inherent advantages and disadvantages which depend to a large degree on their particular application. The objective of this paper is an attempt to evaluate critically these existing concrete constitutive relations and failure criteria within the context of their use in the numerical analysis of concrete structures and to determine the range of their applicability, relative merits, and limitations and to identify the specific need for further modifications and developments.