Fossil fuel resources (eg, coal, oil, and natural gas) exist in underground reservoirs, where discontinuities are widespread and influence the stability of rock structures. The mechanical behavior of jointed rock masses significantly affects the long‐term stability of rock engineering. A major challenge in this area is to link the time‐dependent deformation with damage influence induced by distribution of joints in rock masses. In this paper, a damage mechanical theory is adopted which deals with several groups of joints distributed in rock masses. Based on the geometrical distribution of joints, a damage model considering the influence of normal vector and area density of joints is used to describe the discontinuities. A damage rheological model for jointed rock masses is developed and programmed in the finite difference software FLAC^3D, and an example of jointed rock masses is used to verify the validity of the model. The damage rheological model could predict the visco‐elastic strain which corresponds to primary creep property, visco‐plastic strain which corresponds to steady state creep property, and damage strain which reflects the damage effect of joints to rock masses. Finally, we use this model to predict the displacements and damage zones in the rock masses surrounding an underground opening.