The auxiliary equation method for the construction of deformed solitary solutions to the mathematical model of tumor-immune system interaction is presented in this paper. The investigated model does not admit classical solitary solutions. Special techniques based on symbolic computations are used to construct deformed solitary solutions by simultaneously avoiding the inherent additional constraints to the model parameters. It is demonstrated that the introduction of the auxiliary equation does not drop any solutions from the original system. Also, deformed solitary solutions do not depend on the parameters of the auxiliary equations. Analytical and computations experiments are used to demonstrate the efficacy of the proposed method.