A theoretical approach to determine the static dipole polarizabilities of carbon buckyonions is presented. The microscopic electronic structure of the system is provided by an effective one-electron model and the screening effects are treated within the random phase approximation (RPA). The particular spherical geometry of these multishell fullerenes makes possible the use of electrostatic arguments to derive a simple expression for the RPA which gives the polarizability of the buckyonion and the dipole moment induced on each shell in terms of either the screened or unscreened polarizabilities of the isolated shells. A systematic analysis as a function of the buckyonion size is performed. The relevance of an adequate microscopic description of the electronic structure is demonstrated by contrasting the results provided by two different representations of the electron motion, namely a surface electron gas and a more realistic Huckel model. A comparison between our results and those derived from classical dielectric models is also performed. (C) 2003 American Institute of Physics.