A constitutive creep model for single crystal ice has been formulated based on the experimental results and the mechanism of the multiplication process of mobile dislocations. In this model, the primary mechanism is considered to be the dislocation motion on the basal planes of single crystal ice due to strong creep anisotropy. The preferred crystallographic orientation and temperature of single crystal ice are incorporated in describing both the elastic and the inelastic deformations in the creep model, Material properties used in the model are the dislocation velocity and the changing dislocation density of single crystal ice based on experimental data. The proposed uniaxial creep model is extended to a biaxial model by allowing inelastic deformation only along the basal planes. Parametric studies are performed to better understand the dependence of macroscopic stress-strain curves on microstructural parameters. The results show strong influence of the loading rate and stress level. Comparison of the model predictions with experimental data shows excellent agreement over a range of strain rates.