Many of the oncolytic viruses used in cancer therapies are rapidly eliminated by the immune response of the host (tumor-bearing hosts may have partially intact immune antiviral mechanisms). This diminishes their anti-tumor effect. However, recent experimental results have shown that the treatment of a particular type of skin cancer with two viruses that express the same tumor associated antigen, extends the survival rate of mice. Here, we derive a mathematical model to investigate the interactions among immune cells, cancer cells, and two different viruses. We use experimental data from our lab to validate the model and estimate parameter values. This allows us to discuss conditions that lead to tumor growth and to propose hypotheses for tumor elimination which can be tested experimentally. In particular, we suggest that the use of oncolytic viruses can only ensure a temporary elimination of cancer cells. Complete cancer elimination can happen only in the presence of activated immune cells.