A unified constitutive model is proposed to describe the mechanical behavior of weak sandstone at different time scales. The instantaneous behavior of this material is characterized by the Drucker-Prager elastoplastic model, while the time-dependent deformation is described in terms of the microstructure evolution. This evolution is numerically simulated by progressive degradation of the elastic modulus and failure strength of the material. The proposed model is used to simulate the instantaneous triaxial compression and the multi-loading creep tests. Generally, good concordance is obtained between numerical simulations and experimental data. The proposed model is capable of describing the main features of these rocks, particularly irreversible deformations, pressure dependency, volumetric transition between compaction and dilatancy, and creep behavior.