The Hartree-Fock-Roothaan theory of atomic and molecular Compton profiles has been presented. Calculations reduce to evaluating molecular Compton profile integrals. An analytical and general formula has been derived for molecular Compton profile integrals. Computer programs have been constructed for molecular Compton profiles. Using these programs, Compton profiles of test molecules CH4, H2O and CO2 have been calculated for a wide range of incident photon energy. Results obtained for Compton profiles of these molecules agree with those in the literature.