Two-stroke poppet-valved engines may combine the high power density of two - stroke engines and the low emissions of poppet-valved engines. A two-stroke diesel engine can generate the same power as a four-stroke engine of the same size, but at higher (leaner) air/fuel ratios. Diesel combustion at high air/fuel ratios generally means hydrocarbons, soot and carbon monoxide are oxidised more completely to water and carbon dioxide in the cylinder, and the opportunity to increase the rate of exhaust gas recirculation should reduce the formation of nitrogen oxides (NOx). The concept is being explored as a means of economically modifying diesel engines to make them cleaner and/or more powerful. This study details the application of two computational models to this problem. The first model is a relatively simple thermodynamic model created by the author capable of rapidly estimating the behaviour of entire engine systems. It was used to estimate near-optimum engine system parameters at single engine operating points and over a six-mode engine cycle. The second model is a detailed CFD model called KIVA-ERC. It is a hybrid of the KIVA engine modelling package developed at the Los Alamos National Laboratory and combustion and emissions subroutines developed at the University of Wisconsin-Madison Engine Research Center. It was used for detailed scavenging and combustion simulations and to provide estimates of emissions levels. Both models were calibrated and validated for four-stroke cycle operation using experimental data. The thermodynamic model was used to provide initial and boundary conditions to the KIVA-ERC model. Conversely, the combustion simulations were used to adjust zero-dimensional combustion correlations when experimental data was not available. Scavenging simulations were performed with shrouded and unshrouded intake valves. A new two-zone scavenging model was proposed and validated using multidimensional scavenging simulations. A method for predicting the behaviour of the two-stroke engine system based on four-stroke data has been proposed. The results using this method indicate that a four-stroke diesel engine with minor modifications can be converted to a two-stroke cycle and achieve substantially the same fuel efficiency as the original engine. However, emissions levels can not be predicted accurately without experimental data from a physical prototype. It is therefore recommended that such a prototype be constructed, based on design parameters obtained from the numerical models used in this study.