This paper considers the optimal design and operation of electrodialysis (ED) desalination plants. In general an ED plant aims to produce potable water from a high salinity source, like brackish water or high salinity water. The system is modelled mathematically as mixed-integer non-linear programming (MINLP) optimization problem, determining the number of desalination stages, the membrane area, the total required energy so as to minimise the total annualised cost of the investment accounting for both infrastructure and operating costs. Two examples from the literature illustrate the applicability of the proposed approach and evaluate the quality of the results obtained.