Molecular modelling using semiempirical methods AM1, PM3, PM5 and, MINDO as well as the Density Functional Theory method BLYP/DZVP respectively were used to calculate the structure and vibrational spectra of d-glucose and d-fructose in their open chain, α-anomer and β-anomer monohydrate forms. The calculated data show that both molecules are not linear; ground state and the number for the point-group C is equal to 1. Generally, the results indicate that there are similarities in bond lengths and vibrational modes of both molecules. It is concluded that DFT could be used to study both the structural and vibrational spectra of glucose and fructose.