To meet the growing trend of electrification of mechanical systems, this paper presents a compactly integrated electric motor and hydraulic pump. The proposed application for this machine requires high flow rates at low pressure differentials and four quadrant operation. The hydraulic pump architecture selected for this machine is a radial ball piston pump. An inside impinged version of this architecture allows for efficient filling of the chambers and is radial balanced, both of which allow high-speed operation for increased power density. The radial ball piston pump is less expensive to manufacture and is radially more compact than a standard radial cylindrical piston pump. A model of the pump and the integrated electric motor have been created to study scaling relationships and drive detailed design and optimization. The scaling study considers how displacement is affected by pump diameter, and how the diameter and required torque change with angular velocity. The detailed model considers the effect of valve timing, piston-cylinder clearance, and pump geometry on the efficiency. The model is then exercised in an optimization of the machine parameters.