Exciton confined in a spherical core/shell nanostructure is studied in the framework of the envelope function approximation. Finite height barriers are used to describe conduction and valence band offsets between core and shell of the structure. Electron and hole effective masses mismatch between core and shell and dielectric mismatch at the surface where core and shell materials meet are taken into account. Exciton ground state energy is determined via the Ritz variational principle using a trial wave function where the coulomb attraction between electron and hole is considered. The theoretical approach developed is applied to determine the coulomb correlation parameter, the binding energy and the spatial extension of a bound electron-hole pair as functions of the core to shell radii ratio for CdS/HgS core/shell nanostructures immersed in aqueous or organic solution.