The spatial dynamics between cancer cells and oncolytic viruses is still poorly understood. We present here a stochastic agent-based model describing infected and uninfected cells for solid tumours, which interact with viruses in the absence of an immune response. Two kinds of movement, namely undirected random and pressure-driven movements, are considered: the continuum limit of the models is derived and a systematic comparison between the systems of partial differential equations and the individual-based model, in one and two dimensions, is carried out. Furthermore, we study the one-dimensional traveling waves of the two populations, with the uninfected proliferative cells trying to escape from the infected cells. In the case of undirected movement, a good agreement between agent-based simulations and the numerical and analytical results for the continuum model is possible. For pressure-driven motion, instead, we observe a wide parameter range in which the infection of the agents remains confined to the center of the tumour, even though the continuum model shows traveling waves of infection; outcomes appear to be more sensitive to stochasticity and uninfected regions appear harder to invade, giving rise to irregular, unpredictable growth patterns. The agreement between the discrete and continuum models can be recovered by increasing the number of agents, but this may compromise the biological meaning of the parameters. Our results suggest that the presence of spatial constraints in tumours' microenvironments limiting free expansion has a very significant impact on virotherapy. Some of these situations allow us to qualitatively reproduce patterns observed in experiments in vitro, suggesting that stochastic events may play a central role in the use of oncolytic virotherapy.