This thesis describes the development of a one-dimensional internal combustion engine simulation program for the Pivotal two-stroke engine. The Pivotal two-stroke engine has many features in common with the standard reciprocating piston engine, but differs in its novel kinematics, which are based around a four bar linkage. The new engine arrangement opens up many new design options and required a flexible and specific simulation tool for research and development. The initial project goals were to develop a simulation code, validate the code against engine data and develop a user interface for easier application. However, it was not possible to realise all of these goals and the project was mostly concerned with the development of the simulation numerical code. Validation will be required before the simulation tool can be used with confidence. Engine simulation is a relatively mature field of research and the simulation program includes many established standard methods. The simulation incorporates a standard single zone thermodynamic cylinder model and a Riemann quasi-one-dimensional finite volume gas dynamics scheme, which includes total variation diminishing variable extrapolation. The calculation of flow through valves uses standard equations for orifice flow and the application to pipe boundary conditions utilises the propagation of characteristic information out of the pipe boundary. Simulation of reed valve deflection has been implemented with the finite element method using direct integration in time. The entire code has been implemented in the Fortran programming language using Compaq Visual Fortran 6.5. To establish a flexible simulation the program has been devised so that the input text data file determines the arrangement of the engine, allowing most engine configurations to be modelled with the one simulation tool. Summary data, including engine power, is outputted to a text file, which can be read by any text editor. Detailed simulation results are written to Matlab mat-files, which require Matlab 5.3, or greater, to open and analyze. In its current form the simulation code is capable of running arbitrary engine arrangements, including the Pivotal engine, and can predict the performance of these engines. However, the code is un-validated against real engine data. Where possible sub-models have been tested and proven against special test cases that have an analytic solution. The next logical extension beyond the current project is to thoroughly validate and compare the engine simulation against real engine test data. Other areas in which the code could be improved include; extending the simulation code to incorporate more advanced models and improving the ease with which engine simulations can be set-up, run and analysed.