Aim: development of a mathematical model for non-invasive mammary duct tumor. Methods: the model was developed using the apparatus technique of ordinary differential equations and partial differential equations. The gland duct is represented by a hollow cylindrical tube inside which the afunctional tissue growth occurs. Results: initial boundary value problems were set for differential equations; stability limits of stationary solutions were determined; an option of the mathematical model for treatment was proposed; conditions for the existence of autowave solutions were found, and numerical solutions were constructed. Conclusion: on the basis of the developed model, an estimate of the tumor growth rate was given; a treatment option was proposed, and an explanation of the reasons for a possible recurrence of the disease was given.