We present TARDIS - an open-source code for rapid spectral modelling of supernovae (SNe). Our goal is to develop a tool that is sufficiently fast to allow exploration of the complex parameter spaces of models for SN ejecta... This can be used to analyse the growing number of high-quality SN spectra being obtained by transient surveys. The code uses Monte Carlo methods to obtain a self-consistent description of the plasma state and to compute a synthetic spectrum. It has a modular design to facilitate the implementation of a range of physical approximations that can be compared to asses both accuracy and computational expediency. This will allow users to choose a level of sophistication appropriate for their application. Here, we describe the operation of the code and make comparisons with alternative radiative transfer codes of differing levels of complexity (SYN++, PYTHON, and ARTIS). We then explore the consequence of adopting simple prescriptions for the calculation of atomic excitation, focussing on four species of relevance to Type Ia supernova spectra - Si II, S II, Mg II, and Ca II. We also investigate the influence of three methods for treating line interactions on our synthetic spectra and the need for accurate radiative rate estimates in our scheme. (read more)