This paper presents a methodology for estimating the minimum design vapor pressure of prismatic pressure vessels for on-ship application. Engineering authorities guide the codes for a novel concept design such as a prismatic pressure vessel using a design by analysis (DBA). DBA methods enable high efficiency because they directly calculate the loads to avoid inherent conservativeness that exists in a design by rule (DBR). However, in DBA methods, the designer should conduct a finite element analysis (FEA) and evaluate the results iteratively to meet the design criteria. In this paper, we propose a new approach to estimating the minimum vapor pressure of a prismatic pressure vessel that follows the design philosophy of an IMO Type C independent tank. The procedure of the proposed method was demonstrated based on a case study. An FEA was also conducted for verification purposes. The results show that the proposed method can effectively estimate the required minimum shell thickness and designed vapor pressure without conducting an iterative FEA. In addition, minimization of the tank shell thickness is made possible because the proposed method directly calculates the crack propagation rate to avoid an unnecessary margin while satisfying the fatigue crack propagation criteria.