Molecular dynamic simulations of pure dimethyl sulfoxide, DMSO (216 molecules) and its "infinitely diluted solutions" of Na + and CI-(1 ion and 215 solvent molecules) have been performed at 298.15 K in NVT ensemble by using a force field model introduced by Liu, Mtiller-Plathe and van Gunsteren (J. Amer. Chem. Sot., 117 (1995) 4363) and a potential of shifted force. The structure of the solutions is discussed in terms of radial distribution functions, orientation of the DMSO molecules, and their geometrical arrangement in the first solvation shells. Dynamics of the first and second solvation shells are studied in terms of mean square displacement of the centre-of-mass of DMSO molecules, and the reorientational autocorrelation functions of dipole moment and S-O bond vectors. It is found that the first solvation shell of Na + consists of 6 DMSO molecules located at the vertices of a distorted oetahedron and oriented by their polar S-O bonds towards the cation with a preferable angle of 156 ° between S-O and Na-S vectors. Translational and reorientational mobilities of the DMSO molecule within the first solvation shell of the cation are significantly lower than in the bulk solvent. The first solvation shell of CI-does not indicate a regular polygonal arrangement. It consists of 10 DMSO molecules oriented by their methyl groups and sulphur atoms towards the anion with a preferable angle of about 90 ° between the bisector of ZCSC and the vector pointing from C1-to the median point between two methyl groups. The dynamic behaviour of the solvent molecules in the first solvation shell of the anion and in the bulk solvent are found to be similar.