Reducing soot emissions from combustion processes is important due to the negative health and environmental effects of atmospheric soot. In order to achieve this goal, there has to be a fundamental understanding of the mechanisms of soot formation to allow for the determination of economically viable methods of reducing these emissions. Due to the highly complex nature of soot formation, detailed numerical models are employed to gain fundamental understanding of the factors that affect each mechanism of soot evolution. Since most practical combustion devices operate at elevated pressures, it is important to understand the effect of pressure on soot formation. The overall goal of this thesis is to improve the currently employed models by replacing tunable constants with fundamental physics, with secondary goals of applying the model to high pressure conditions. This thesis is divided into four research studies. The first is a detailed description and validation of the numerical code utilized to simulate soot formation, denoted as the CoFlame code. The second study develops a novel model for two key soot formation processes, which are the polycyclic aromatic hydrocarbon (PAH) nucleation and condensation processes. The novel reversible PAH clustering (RPC) model is shown to be superior to previous models. The third study enhances the RPC model to include nucleation and condensation events from a wide range of PAHs. It is shown that smaller PAHs contribute the most to the nucleation process, while all PAHs contribute to the condensation process. The fourth and final study applies the CoFlame code to high pressure flames and determines that shear between the air and fuel streams is responsible for the formation of recirculation zones at elevated pressures and complete conversion of fuel to soot.