The linear uniform field electric dipole polarizability tensors of 46 fullerenes in the range C-20 through C-240 are calculated by the Olson-Sundberg atom monopole-dipole interaction (AMDI) theory, using the monopole and dipole polarizabilities of the carbon atom found previously to fit polarizability tensors of aromatic hydrocarbons. The structures are taken to be those predicted by Zhang and co-workers by molecular dynamics energy optimization. The isotropic mean polarizabilities calculated for C-60 and C-70 are comparable to experimental data from solid film studies and to quantum mechanical calculations. Polarizability tensors are also calculated for conducting ellipsoidal shells which have the same moment of inertia tenser as the corresponding fullerenes. These are substantially smaller than the AMDI polarizabilities for the smaller fullerenes, but the two calculations tend to converge for the larger molecules.