The number of sub-populations of tumour cells constituting a tumour and the immunogenicity of tumour cells are two major components of intra-tumour heterogeneity (ITH), and play a key role in the immune response against solid tumours. Mathematical models make it possible to separate these two components of ITH and investigate their influence on anti-tumour immunity in a controlled manner. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8 + T cells. We use this model to investigate how ITH may affect the anti-tumour immune response. In our model, ITH can vary both with the number of expressed antigens (i.e. the number of sub-populations of tumour cells) and with the level of antigen presentation (i.e. the immunogenicity of the cells). Computational simulations of our model indicate that both sources of ITH affect the outcome of anti-tumour immune response. First, the number of sub-populations of tumour cells negatively correlates with the ability of the CD8 + T cells to produce an efficient anti-tumoural response. Second, the fraction of non-immunogenic cells within a tumour can significantly reduce the effectiveness of the immune response. These results qualitatively reproduce a broad range of scenarios of successful and unsuccessful immune surveillance reported in experimental studies. Ultimately, our model may provide a framework to help biologists and clinicians to better understand the prognostic outcomes of immunotherapy.