Abstract: For the research ondynamic failure of major civil structures, constitutive modelingof concrete is one of its key scientific issues. The constitutivemodels of concrete subjected to static action or dynamicexcitation are reviewed in the present paper. The knowledge anddevelopment of constitutive models is discussed based on itshistorical developments and logical relations. Damage model ofconcrete which has been developed in recent years is summarized atmacro and micro levels. The development trends of constitutivemodeling for concrete are suggested on the basis of ourunderstanding of essential physical properties of concrete, e.g.its nonlinearity and randomness.