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 latter 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 ensure a quasi-stable configuration of the system. The model is applied to three nuclear molecules, namely ⁹⁶Sr + ¹⁰Be + ¹⁴⁶Ba, ¹⁰⁸Mo + ¹⁰Be + ¹³⁴Te and ¹¹²Ru + ¹⁰Be + ¹³⁰Sn.