Utilizing a point-dipole interaction model, we present an investigation of the static polarizability and second hyperpolarizability of fullerenes and carbon nanotubes by varying their structure. The following effects are investigated: (1) the length dependence of the components of the static polarizability, (2) the static second hyperpolarizabilities Of C-60 and C-70, (3) the symmetry effects on the static second hyperpolarizability, (4) the length dependence of the components of the static second hyperpolarizability, and (5) the diameter dependence of the static second hyperpolarizability. It is demonstrated that the carbon nanotubes exhibit significantly larger second hyperpolarizabilities compared to a fullerene containing the same number of carbon atoms. Furthermore, the calculations show that the carbon nanotubes have a much larger directionality of the static second hyperpolarizability than the fullerenes.