Abstract: By mean of the basic principle of classical plasticity theory, a new constitutive model for concrete is proposed, which do not comprises formal hypotheses of a yield surface and a failure criteria. Moreover, the typical unified viscoplastic constitutive model only used to analyze the metal materials is developed as well. The two hypotheses of typical unified viscoplastic constitutive theory is given up that the accumulated inelastic strain does not produce a significant change in the volume and the accumulated inelastic strain and strain rate appear to be independent of hydrostatic stress. The physical meaning of plastic multiplier is extended. Simultaneously, its expression of continuous function is given. The results from numerical simulation show that this model is capable of reproducing the significant deformation phenomena, including strain-rate sensitivity, volume dilatancy under compression, and stiffness degradation and strain-softening behavior beyond the peak stress induced by damages and fractures.