Due to the rock skeleton structural deformation and body deformation in the exploitation of unconsolidated sandstone gas reservoir, permeability and porosity become lower and make strong stress sensitivity，which results in that the well test data can not be accurately explained by the conventional well test model. A mathematical model of homogeneous circular gas reservoir with closed border in consideration of stress sensitivity is presented, and the typical curves are analyzed. The research shows that the stress sensitivity appears in the latter part of the pseudo-steady stage, and the index change in relations between permeability and pressure has a clear impact on the dynamic test results only when B>0.1MPa- 1. The upwarping feature of pseudo-pressure is similar to the well test model of sandstone gas reservoir which does not have stress sensitivity and impermeable boundary. The well test model which considers the stress sensitivity can be used to analyze the well test data in unconsolidated sandstone gas reservoirs and provides some guidance for these reservoirs exploitation.