Obtaining a theoretical solution for the response of plate structures to arbitrarily shaped pressure pulses is often difficult. For engineering purposes, arbitrarily shaped pressure pulses are often simplified to equivalent rectangular pressure pulses to calculate the theoretical responses of the plate structures. Therefore, the semi-empirical method proposed by Youngdahl is often used. Although the effectiveness of Youngdahl's method has been verified in small deformation cases, the method lacks a theoretical explanation of the equivalence basis for cases of large deformation. In this paper, a method based on the membrane theory (MEM) is established for equivalence between arbitrarily shaped pressure pulse applied on circular plate and rectangular pressure pulse, and the differences and similarities between the MEM and the Youngdahl's equivalent method (YEM) are analyzed. Using the membrane theory, the responses of five different pressure pulses are compared, revealing that the pulse shape has a significant influence on the theoretical deformation obtained by the membrane theory. Then, a load equivalent method based on the membrane theory is proposed. In particular, for a linearly decaying pressure pulse, an analytical solution of the equivalent load is provided, and the equivalent pressure and pulse duration of the MEM and YEM are calculated. Notably, the pressure and pulse duration obtained by the MEM under the large deformation theory significantly differ from those obtained by the YEM. A numerical simulation indicates that the response errors of the equivalent load relative to the original linearly decaying pressure pulse of the two methods are close, both within the acceptable range of engineering. The theoretical analysis shows that the product of the characteristic frequency of the membrane response and pulse duration — a dimensionless number — affects the relative magnitude of the equivalent pressure of the YEM and MEM. When the final deformation time occurs after the duration of the linearly decaying pressure pulse, the deformation of the circular plate under the equivalent load obtained by the YEM is greater than that obtained by the MEM.