This paper analyzes the stability of the dynamic coupling among the homogeneous charge compression ignition (HCCI) combustion, gas exchange dynamics and the piston dynamics in a hydraulic free piston engine. The intrinsic feedback nature of the system makes the stability of the engine operation difficult to predict. Specifically, output from the gas exchange process of the previous cycle affects the combustion timing of the current cycle. The combustion force and hydraulic loading together determine how far the piston can travel (dead center positions) and provide input for the current cycle gas exchange process. A discrete cycle-to-cycle based model that captures this dynamic coupling is described in the paper. Linearization of the model gives us the insight of the engine stability under any given operation conditions. The stability analysis is validated with Matlab numerical simulation results of a high-order nonlinear model under a specified set of operation conditions. The proposed methodology can be transformed and applied to analyze stability of systems with similar dynamics couplings.