Most of the underground gas storage （UGS） facilities built in China are rebuilt from sandstone gas reservoirs. They are subjected to increased risks of sand production due to the cumulative alternating damage to the reservoir rock structure after multi-cycle alternating injection and production. In order to effectively predict sand production risks，an alternating mechanics experiment considering multi-parameter sensitivity was designed by combining the stress field of the borehole wall of the injection-production well and the shear failure criterion of rocks. Based on the alternating mechanics experiment，the degree of rock strength damage was calculated，and a sand production critical drawdown pressure model based on rock damage degree was proposed. Research showed that the stress field of the reservoir dynamically changes with the production of the gas storage，resulting in a change in the difference between the circumferential and radial stresses of the surrounding rock of the borehole wall of the injection-production well. At the same time，the stress difference also changes along the wellbore circumference. Under the alternating loads，the cumulative damage of rocks grows with the increasing water saturation （for the same particle sizes of rocks） and larger particle sizes of rocks （for the same water saturations of rocks）. The sand production critical drawdown pressure predicted using the proposed method is 11.41 MPa in the early stage of gas production and 3.97 MPa in the late stage. This study provides a new method for determining experimental parameters in alternating mechanics，as well as a new method for judging sand production in alternating injection and production for UGS facilities to guide the UGS production planning and control.