The need for reduced CO2 emissions has motived new and novel designs to maximize engine efficiency, reduce weight, and increase engine performance. One such engine design was proposed by Jones Engine LLC, which utilizes a novel toroidal piston/cylinder configuration, eliminating the connecting rod of the traditional slider-crank mechanism. This design enables a more direct transfer of work to the crankshaft and reportedly produces significantly increased torque, reduced fuel consumption, and decreased engine weight. This work seeks to model the Jones Engine's unique engine cycle, and directly compare to analogous conventional slider-crank engines to provide an assessment of the benefits and limitations of the Jones Engine concept. In this work, the Jones Engine concept was modeled via a MATLAB-based 0-D engine simulation code developed by the authors, utilizing Cantera to solve gas phase chemical kinetics. The engine was modeled in two combustion modes, Homogeneous Charge Compression Ignition (HCCI), and Spark-Ignition (SI). The HCCI combustion model utilized a homogeneous single-zone model, while the SI combustion model utilized a 2-zone approach, and these models were validated against experimental data from literature. The results of the simulations showed that at identical engine operating conditions and analogous geometries, the Jones offered slightly reduced efficiency in HCCI and SI combustion modes, but with significantly higher output torque due to the Jones Engine mechanism. Results also showed increased knock mitigation for the Jones Engine in SI mode, and therefore the ability to operate with significantly higher geometric compression ratios.