Experimental data suggest that in ionic solid solutions the bond-length mismatch is partially accommodated by microscopic lattice distortions. In this paper we study the structural properties of ionic alloys using a generalized Born - Mayer energy model accounting for the possibility of atomic-scale relaxations. Cubic supercells are used to simulate the real random alloys, providing statistical information about the atomic distribution and interatomic distances. The good agreement with the available experimental data and with the results of ab initio pseudopotential calculations performed for comparison for some selected systems indicate the validity of the model here employed. We also discuss the applicability to ionic alloys of the special quasi-random structures originally proposed for semiconducting alloys.