Based on the concept of shear-induced anisotropic degradation, a model involving time dependent behavior is proposed to simulate the deformational characteristics of weak sandstone. The stress-strain relationship of the proposed model was originated from the degradation of moduli K and G subjected to different loading conditions. An anisotropic factor β is introduced to indicate the tendency of shear-induced volumetric deformation. Furthermore, to incorporate time-dependent deformation behavior of sandstone, this anisotropic degradation model is further extended using a generalized Burger's model. As a result, this proposed constitutive model is characterized by the following features: (1) being capable of describing shearinduced volumetric deformation, either compression or dilation, prior to the failure state; (2) being versatile in the time-dependent (creep) deformations (3) the anisotropic factor β serves as a convenient index regarding whether shear-induced volumetric deformation dilates or not; and (4) the number of material parameters is controlled to be as few as possible. The proposed model has been verified by comparing to experimental results. It is found that the proposed model is versatile in simulating short-term and long-term deformations of sandstone under different stress paths.