Molecular dynamics (MD) simulations of pure dimethyl sulphoxide (DMSO) and solutions of Na+, Ca2+, Cl−, NaCl and CaCl2 in DMSO have been performed at 298.15 K and 398.15 K in NVT ensembles by using a four-interaction-site model of DMSO and reaction field method for Coulombic interactions. The structure of solvent, ion-solvation shells and ion-pairs have been analysed by employing a concept of coordination centres and characteristic vectors of the solvent molecule. Results are given for atom-atom (corresponding to DMSO), ion-atom and ion-ion radial distribution functions (RDFs), orientation of the DMSO molecules and their geometrical arrangements in the first solvation shells of the ions (Na+, Ca2+, Cl−). A preferential formation of cyclic dimers with antiparallel alignment between dipole moments of nearest-neighbour molecules in the pure solvent is found. Geometrical models of the first coordination shells of the ions in ‘infinitely dilute solutions’ are proposed. Ion-ion RDFs in NaCl-DMSO and CaCl2-DMSO solutions reveal the presence of both solvent separated (SSIP) and contact (CIP) ion pairs. The structures of the solvation shells of such ion pairs are also discussed.