Series hybrid electric vehicles (HEVs) require power-plants that can generate electrical energy without specifically requiring rotary input shaft motion. A small-bore working prototype of a two-stroke spark ignited linear engine-alternator combination has been designed, constructed and tested and has been found to produce as much as 316W of electrical energy. This engine consists of two opposed pistons (of 36 mm diameter) linked by a connecting rod with a permanent magnet alternator arranged on the reciprocating shaft. This paper presents the numerical modeling of the operation of the linear engine. The piston motion of the linear engine is not mechanically defined: it rather results from the balance of the in-cylinder pressures, inertia, friction, and the load applied to the shaft by the alternator, along with history effects from the previous cycle. The engine computational model combines dynamic and thermodynamic analyses. The dynamic analysis performed consists of an evaluation of the frictional forces and the load (in this case the alternator load) across the full operating cycle of the engine. The thermodynamic analysis consists of an evaluation of each process that characterizes the engine cycle, including scavenging, compression, combustion and expansion, based on the first law of thermodynamics. Since the modeled engine was crankshaftless, a time-based Wiebe function (as opposed to a conventional crank angle-based approach) was used to express the mass fraction burned for the combustion process, while the combustion model used was a single-zone model. To render the model useful, the parameters used were based on experimental data obtained from the working example, including instantaneous shaft position, velocity and in-cylinder pressure. Also, a parametric study was performed to predict the behavior of the engine over a wide operating range, given variations in fuel combustion properties, the reciprocating mass of the piston shaft assembly, frictional load and the externally applied electrical load.