A floating-stroke, free-piston internal combustion reciprocating engine (FS-FPE) is currently under development with the primary goal of high engine efficiency, along with ultra-low emissions. High compression ratio, boosted, lean operation is targeted with kinetically-modulated combustion expected to be utilized as a principal mode of operation. To aid the engine's preliminary design stage modeling is conducted in order to explore the engine's operational characteristics and charge conditioning needs. Natural gas and gasoline are considered as potential fuels. A single-zone, homogeneous reactor model (HRM) is employed to approximate the in-cylinder processes, especially the ignition chemistry (timing) which is important for operation under these conditions. Sub-models are integrated into the HRM to describe fuel evaporation, heat transfer, and piston crevice / ringpack flows. A range of operating parameters is explored including fuel loadings (ϕ = 0.25 to 0.55), piston speeds (1200 to 4800 cycles per minute), intake pressures (p = 0.5 to 2.0 bar), and intake temperatures (T = −60 to 130C). The engine design and results of this modeling study are presented here.