Replication-competent viruses based on the Edmonston vaccine strain of measles virus (MV-Edm) have potent and selective activities against various types of tumours in vitro but the responses in vivo are more variable. Some tumours are eliminated consistently while others persist despite evidence of ongoing viral propagation. In order to understand these disparate results, we have developed a model for the spatial growth of a tumour population followed by infection with a replicating virus that can spread by cell-to-cell fusion ultimately leading to cell death. We utilize the model to explore both the impact of tumour architecture and the dynamics of tumour cell-virus interactions on the outcome of therapy.