This paper introduces a Hydraulic Linear Engine (HLE) concept and describes a model to simulate instantaneous engine behavior. The United States Environmental Protection Agency has developed an HLE prototype as an evolution of their previous six-cylinder, four-stroke, free-piston engine (FPE) hardware. The HLE design extracts work hydraulically, in a fashion identical to the initial FPE, and is intended for use in a series hydraulic hybrid vehicle. Unlike the FPE, however, the HLE utilizes a crank for improved timing control and increased robustness. Preliminary experimental results show significant speed fluctuations and cylinder imbalance that require careful controls design. This paper also introduces a model of the HLE that exhibits similar behavior, making it an indispensible tool for controls design. Further, the model's behavior is evaluated over a range of operating conditions currently unobtainable by the experimental setup.