One of the main challenges for the practical implementation of dielectric elastomer generators (DEGs) is supplying high voltages. To address this issue, systems using self-priming circuits (SPCs) — which exploit the DEG voltage swing to increase its supplied voltage — have been used with success. A self-priming circuit consists of a charge pump implemented in parallel with the DEG circuit. At each energy harvesting cycle, the DEG receives a low voltage input and, through an almost constant charge cycle, generates a high voltage output. SPCs receive the high voltage output at the end of the energy harvesting cycle and supply it back as input for the following cycle, using the DEG as a voltage multiplier element. Although rules for designing self-priming circuits for dielectric elastomer generators exist, they have been obtained from intuitive observation of simulation results and lack a solid theoretical foundation. Here we report the development of a mathematical model to predict voltage boost using self-priming circuits. The voltage on the DEG attached to the SPC is described as a function of its initial conditions, circuit parameters/layout, and the DEG capacitance. Our mathematical model has been validated on an existing DEG implementation from the literature, and successfully predicts the voltage boost for each cycle. Furthermore, it allows us to understand the conditions for the boost to exist, and obtain the design rules that maximize the voltage boost.