A boundary-value problem for electrodialysis with ion-exchange membranes is posed and its analytical solution obtained. The solution allows one to calculate concentration fields in desalination and brine compartments, the current-density distribution along the flow coordinate and the thickness of diffusion boundary layers. It also makes it possible to estimate the value of local limiting current-density and to obtain the dependence of the process on physico-chemical characteristics of ion-exchange membranes (transport numbers and conductivity). The mathematical model was verified by a local distributive analysis made by means of laser interferometry.