Abstract: Due to the intrusion of foreign fluid, mud shale presents obvious rheological effect, so borehole collapse tends to happen easily. In order to investigate how the borehole stability in mud shale is affected by viscoelastic mechanical behavior which is caused by fluids in the well, a viscoelastic creep constitutive model was developed to show the mechanical mechanisms and evolution laws of borehole rheological instability and deterioration. Then, balance equation and geometric equation were derived according the force on the surrounding rocks of borehole. Combined with the physical equation and boundary conditions, the drilling fluid density equation based on viscoelastic characteristics of shale was established. And finally, density charts of drilling fluids in mud shale with different shrinkage rates over the time were plotted based on actual drilling data. It is indicated that the lower the borehole shrinkage rate is, the higher the drilling fluid density shall be. As the well depth and drilling time increase, the density of drilling fluid shall be increased.