Stress sensitivity effect widely exists in low permeability gas reservoir development process. In order to research unstable seepage characteristics of low permeability gas reservoir in stress sensitivity conditions, established is an unsteady seepage flow model based on the stress sensitivity effect and a real space solution is obtained through model solution and Stehfest numerical inversion method and analyzed is the effect of stress sensitivity on unstable seepage pressure dynamic characteristics of low permeability gas reservoir with infinite boundary, closed boundary and constant pressure boundary. The results show that the relationship between bottom hole pressure and stress sensitivity is mutual, the effect of stress sensitivity is particularly significant in case of lower bottom hole pressure and the effect of stress sensitivity on low permeability gas reservoir can not be neglected. The above study results can provide valuable reference for well testing analysis and in-site production in stress sensitive gas reservoir.