The goal of this paper is to provide both the basic scientist and the clinician with an advanced computational tool for performing in silico experiments aiming at supporting the process of biological optimisation of radiation therapy. Improved understanding and description of malignant tumour dynamics is an additional intermediate objective. To this end an advanced three-dimensional (3D) Monte-Carlo simulation model of both the avascular development of multicellular tumour spheroids and their response to radiation therapy is presented. The model is based upon a number of fundamental biological principles such as the transition between the cell cycle phases, the diffusion of oxygen and nutrients and the cell survival probabilities following irradiation. Efficient algorithms describing tumour expansion and shrinkage are proposed and applied. The output of the biosimulation model is introduced into the (3D) visualisation package AVS-Express, which performs the visualisation of both the external surface and the internal structure of the dynamically evolving tumour based on volume or surface rendering techniques. Both the numerical stability and the statistical behaviour of the simulation model have been studied and evaluated for the case of EMT6/Ro spheroids. Predicted histological structure and tumour growth rates have been shown to be in agreement with published experimental data. Furthermore, the underlying structure of the tumour spheroid as well as its response to irradiation satisfactorily agrees with laboratory experience.