The hydration structures of five monatomic cations and two monatomic anions are studied by Monte Carlo NpT simulations conducted on infinite dilute aqueous electrolyte solutions. The complete first and second hydration shells are defined by the successive minima of the radial distribution functions’ ion-water oxygen atoms. The first shell structure is determined essentially by the electrostatic charge of the ion and by the short-range ion-water molecule interactions so that it is always constituted by six molecules located at the vertices of regular octahedra unless if the distance between the charge of the ion and the opposite charge in the water molecule is large enough to allow the presence of more than six water molecules. This is the case of the K+ which presents eight molecules in its first shell. The pairs of hydrogen atoms are, in the first shell, preferentially perpendicular. The structure of the second shell is defined by the bulk tetrahedral structure induced by the water molecules so that they are similar for cations and anions. The resulting second shell densities are very close to the pure water density. Both complete hydration shells are maintained stable by means of a compromise between the strong attraction that the ion carry out on the water molecules and by the resulting repulsion between these molecules which are forced to get too close to one another.