Realistic constitutive models for ice are necessary for reliable prediction of ice loads and ice-structure interaction. Previous analytical work has tended to concentrate on ice behavior at low strain rates. Under high strain rates, the post peak softening behavior becomes more important than rate-dependency. This paper proposes a new constitutive model for ice under high strain rates, incorporating strain softening and pressure sensitivity. In its present form, the model is incrementally linear and can be easily implemented in a finite element computer program to solve monotonic loading problems.