ABSTRACTServo-valves or variable displacement pumps are typically used to control conventional hydraulic injection molding machines (IMMs). Recent developments in electrical drive technology allow to utilize servo-motor driven pumps instead, which is beneficial due to their higher energy efficiency. Their dynamic behavior, however, is significantly different compared to the conventional setup. Thus, currently used mathematical models and control concepts cannot be directly applied. This paper presents a computationally efficient and scalable mathematical model of the injection process for these servo-pump driven IMMs. A first-principles model of the injection machine is combined with a phenomenological model describing the injection process, i.e. the compression of the melt and the polymer flow into the mold. The proposed model is tailored to real-time applications and serves as an ideal basis for the design of model-based control strategies. The feasibility of the proposed model is demonstrated by a number of different experiments. They confirm a high model accuracy over the whole operating range for different mold geometries.