Operation of a free piston linear engine is modeled based on the combination of three mathematical models, including a piston dynamic model, a linear alternator model and a thermodynamic model. The simulated in-cylinder pressure, piston velocity, and electric power output are compared with the corresponding experimental results to validate the models mentioned above. The influences of the design parameters, including cylinder dimension ( Le), number of coil turns ( N), and air gap ( g) between the translator and stator, on the dynamic performance, in-cylinder pressure and electric power generation of the free piston linear engine are studied. The study results show that the reduction of Le has a benefit for improving the piston dynamic performance and output electric power, however it also reduced the cylinder pressure. The increase of number of coil turns N results in the reduction of the peak piston velocity, displacement, acceleration, and pressure in the cylinder, however, it increases the output electric power of the free piston linear engine. The peak piston velocity, displacement, acceleration, and pressure in the cylinder are considerably decreased when g is reduced. However, the reduction of g has a benefit to improve the output electric power of the free piston linear engine. The energy conversion efficiency can be maximized when g and Le are reduced, and N is increased.