<p>Owing to their rolling friction, two-dimensional piston pumps are highly suitable as power components for electro-hydrostatic actuators (EHAs). These pumps are particularly advantageous for applications requiring high efficiency and reliability. However, the ambiguity surrounding the output flow characteristics of individual two-dimensional pumps poses a significant challenge in achieving precise closed-loop control of the EHA positions. To address this issue, this study established a comprehensive numerical model that included gap leakage to analyze the impact of leakage on the output flow characteristics of a two-dimensional piston pump. The validity of the numerical analysis was indirectly confirmed through meticulous measurements of the leakage and volumetric efficiency, ensuring robust results. The research findings indicated that, at lower pump speeds, leakage significantly affected the output flow rate, leading to potential inefficiencies in the system. Conversely, at higher rotational speeds, the impact of leakage was less pronounced, implying that the influence of leakage on the pump outlet flow must be carefully considered and managed for EHAs to perform position servo control. Additionally, the research demonstrates that two-dimensional motion does not have a unique or additional effect on pump leakage, thus simplifying the design considerations. Finally, the study concluded that maintaining an oil-filled leakage environment is beneficial because it helps reduce the impact of leakage and enhances the overall volumetric efficiency of the pump system.</p>