The internal blast load in spherical vessels is simplified as a triangle pulse with subsequent quasi-static pressure. Based on the single degree of freedom model, the analytical model of elastic dynamic response of the spherical shell is established and the solution of radial displacement response is obtained. The analytical results and LS-DYNA numerical simulation are in good agreement, and the reliability of the analytical solution is verified. By analyzing the radial displacement response formula, effects of quasi-static pressure on the dynamic response can be studied. It is found that the duration time of the first pulse and the quasi-static pressure have their own critical values, which have decisive influence on the time when maximum displacement occurs. The critical duration time of first pulse is related to the fundamental frequency, and the critical quasi-static pressure is related to multi-factors such as the duration time and the peak overpressure of the first pulse, the fundamental frequency, the thickness of the shell, Young′s modulus and Poisson′s ratio, etc. The maximum displacement increases with the increase of the quasi-static pressure if it occurs in duration of the quasi-static pressure, and it is not affected by the quasi-static pressure if it occurs in the first pulse. The minimum displacement increases with the increase of quasi-static pressure, and the amplitude of subsequent vibration decreases with the increase of quasi-static pressure. The research results show that when using multiple-use explosion containment vessels to make the evaluation of the explosive effect in confined space, not only the specific details of the first pulse and subsequent quasi-static pressure of the blast load should be taken into consideration, but also the structural dynamic response history and structural parameters analysis must be closely integrated.