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This study proposes a new constitutive model to describe the smooth transition from an elastic to a plastic response in sands under monotonic shearing. The model modifies the conventional Mohr–Coulomb model by considering the concept of a bounding surface and critical state soil mechanics. The friction angle consists of the critical state friction angle and a portion of the dilatancy angle, which is determined from the distance to the critical state line. Incorporating the bounding surface and the dilatancy angle into constitutive relationships for Toyoura sand produces numerical simulation results that have good agreement with the experimental results.