Based on the single degree of freedom model, the dynamic elastic-plastic response of a spherical shell subjected to internal impulse with quasi-static pressure is obtained. Analytical solutions agree well with numerical simulation results. The solutions can be divided into two situations by confirming whether the yield point occurs in first triangle impulse or the duration of quasi-static pressure. Effects of quasi-static pressure can be studied in two different situations. If the yield occurs in the quasi-static pressure phase, the time when yield occurs is affected by the quasi-static pressure and decreases with the increase of the quasi-static pressure. Whenever the yield occurs, the maximum displacement occurs in the quasi-static phase, and the time reaching maximum displacement is quite different. The value of maximum displacement increases significantly with the increase of the quasi-static pressure. Compared with the elastic situation, the quasi-static pressure has a more obvious effect in the elastic-plastic response analysis. Therefore, the elastic-plastic dynamic response analysis is more valuable and instructive for the evaluation of quasi-static pressure.