In this article we present a mechanism of self-diffusion in undercooled liquids. There are a number of models for diffusion in disordered systems but none of them describes without contradiction the experimental facts. In general molecular dynamics simulations give the possibility to calculate the diffusion coefficients directly, however for low temperatures computer simulations consume a lot of time even using modem powerful computers. The present model of diffusion in undercooled liquids gives an analytical expression for the diffusion coefficient as a function of temperature, where temperature can vary in a large interval.