Annotation: The article formulates a generalized model of an elastic-viscous fluid, in particular, from this model one can obtain Newtonian, generalized Newtonian, Maxwellka and other models. Basically, the generalized model of a viscoelastic fluid is built on the basis of the topological hypothesis of Astarit and Marrucci and the axiomatic principles of Truesdell and Knoll. The developed generalized model of a viscoelastic fluid is convenient for solving engineering problems and thus is easily implemented for studying the flow of non-Newtonian fluids in a flat channel and in a circular cylindrical tube.