The vibrational excitations of linear triatomic molecules, including both bending and stretching vibrations, are studied in the framework of dynamical symmetry groups. In this framework, the dynamical symmetry group of triatomic molecules is U1(4)⊗U2(4). Hence, a Hamiltonian is constructed that includes the second-order combination of the invariant operators. The eigenvalues of the molecular Hamiltonian give relatively little improvement for HCN but significant improvement for OCS. We obtained highly excited vibrational levels of the two molecules.