<p>The computation of two-points effective resistance is an elegant research problem within theory of electrical network. For any two vertices <i>u</i> and <i>v</i> of a graph <i>G</i> the resistance distance is defined as the effective resistance among the corresponding vertices in an electrical network extracted from <i>G</i> by replacing every edge with a unit resistor. The Kirchhoff index is defined as the sum of resistance distance among all vertices pairs of <i>G</i>. Corresponding to the skeleton of a platonic solid an octahedron is a three dimensional shape which we consider as a polyhedral graph plays a vital role in the synthesis of metal organic frameworks. By applying the techniques and transformations from theory of electrical networks the calculation of effective resistance between all pairs of vertices of chain octahedron structure is the main theme of this paper. By using our results we also compute the Kirchhoff index.</p>