The question of incorporating the notion of point groups in the algebraic Vibron model for molecular rotation-vibration spectra is addressed. Boson transformations which act on intrinsic states are identified as the algebraic analog of the discrete point group transformations. A prescription for assigning point group labels to states of the Vibron model is obtained. In case of nonlinear triatomic molecules the Jacobi coordinates are found to be a convenient possible choice for the geometric counterparts of the algebraic shape parameters. The work focuses on rigid diatomic and triatomic molecules (linear and bent).