Electronic properties and intersub-band optical transition energies are studied in group II to VI wide band gap semiconductors taking into account the geometrical confinement of the core and shell materials. ZnS/CdS, ZnS/CdSe, and CdS/CdSe are some group II to VI core/shell semiconducting materials, which are considered in the present work. The effects of internal electric field, due to spontaneous and piezoelectric polarization, are taken into consideration in the calculations. The dielectric-mismatch effect and the position-dependent effective mass are included in the Hamiltonian. The electronic properties are studied using the variational method and the optical properties are considered using the density matrix approach. All the properties are discussed for various ratios of core and shell radii of the materials in the strong confinement region. The effect of geometrical confinement on the Coulomb interaction energies in the core/shell materials is found. The oscillator strength is computed for these core/shell materials and the optical absorption coefficient as a function of photon energy is investigated in the strong and weak confinement regions. The result shows that the electronic and optical properties are dominant in the strong confinement region.