Due to recent advances in technologies ranging from hydraulically-assisted prostheses to human-scale robotics, there is a growing need for compact and efficient delivery of hydraulic power. Existing electric driven pumps require conversion from electric to rotational power before generating hydraulic output power. This work presents a dynamic model and experimental results of a linear pump that uses an electromagnetic force applied directly to the piston, resulting in a more direct conversion of electrical to hydraulic power in a compact package at the human power level. The model uses a quasi-steady state magnetic equivalent circuit model for the linear electromagnetic actuator coupled to a numerical time-domain piston pump model. The coupled model calculates the piston trajectory, cylinder pressures, and flowrates as a function of time. The modeled force generation and resulting mechanical dynamics match results generated from finite element analysis within 7%, with a predicted power density of 0.19 W/cc and efficiency of 73% for an unoptomized geometry. A multi-objective genetic algorithm is used to determine the geometry and operating parameters that give maximum power density and maximum efficiency, demonstrating that power densities of 0.7 W/cc and efficiencies of 85% are achievable.