A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.