A plasticity model was developed to predict the behavioral characteristics of concrete in multiaxial compression. To extend the applicability of the proposed model to concrete in various stress states, a new approach for failure criteria was attempted. A stress was decomposed into one volumetric and two deviatoric components orthogonal to each other. Three failure criteria wire provided independently for each stress component. To satisfy the three failure criteria, the plasticity model using multiple failure criteria was Implemented. Each failure surface was defined by equivalent volumetric or deviatoric plastic strain. To present dilatancy due to compressive damage a non-associative flow nile was proposed. The proposed model was implemented to finite element analysis, and it was verified by comparisons with various existing test results. The comparisons show that the proposed model predicted well most of the experiments by using three independent failure criteria.