This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page.