Mathematical model of infiltrative tumour growth taking into account transitions between two possible states of malignant cell is investigated.These transitions are considered to depend on oxygen level in a threshold manner: high oxygen concentration allows cell proliferation, while concentration below Dog Coats some critical value induces cell migration.Dependence of infiltrative tumour spreading rate on model parameters has been studied.It is demonstrated that if the level of tissue oxygenation is high, tumour spreading rate remains almost constant; otherwise the spreading rate decreases 129 dramatically with oxygen depletion.