A spheroid is an ellipsoid for which two of the axes are equal, and here the interaction between spheroidal fullerenes and carbon nanotubes is modeled using the Lennard–Jones potential and the continuum approximation. The resulting surface integrals are evaluated analytically for a number of configurations, including lying and standing as well as spheroids with an arbitrary tilt angle, and centered on the nanotube axis. Analytical expressions for off-axis spheroids in all three orientations are also given, and the findings are shown to agree well with previously published work. However, the major contribution of this work is the derivation of new exact analytical formulae to calculate the van der Waals interaction energy for these configurations, and in particular the results for the tilting and off-axis configurations which are far more general than those which have appeared in the literature previously. From these exact expressions, five primary regimes are identified: lying on-axis, tilting on-axis, standing on-axis, standing off-axis and finally lying off-axis. Also identified in this study is a precisely prescribed radius, for the transition between regimes four and five, for which two equally energetically favorable orientations exist and for which these two configurations are separated by a known energy barrier. The notion arises that such configurations may be exploited for nano-scaled memory devices used in nano-computing.