  A geometrical model for tri-nuclear molecules is presented. An analytical
solution is obtained provided the nuclei, which are taken to be prolately
deformed, are connected in line to each other. Furthermore, the tri-nuclear
molecule is composed of two heavy and one light cluster, the later sandwiched
between the two heavy clusters. A basis is constructed in which Hamiltonians of
more general configurations can be diagonalized. In the calculation of the
interaction between the clusters higher multipole deformations are taken into
account, including the hexadecupole one. A repulsive nuclear core is introduced
in the potential in order to insure a quasi-stable configuration of the system.
The model is applied to three nuclear molecules, namely $^{96}$Sr + $^{10}$Be +
$^{146}$Ba, $^{108}$Mo + $^{10}$Be + $^{134}$Te and $^{112}$Ru + $^{10}$Be +
$^{130}$Sn.

Nuclear Theory