  Let $G$ be a connected graph. The resistance distance between any two
vertices of $G$ is equal to the effective resistance between them in the
corresponding electrical network constructed from $G$ by replacing each edge
with a unit resistor. The Kirchhoff index is defined as the sum of resistance
distances between all pairs of the vertices. These indices have been computed
for many interesting graphs, such as linear polyomino chain,
linear/M\"{o}bius/cylinder hexagonal chain, and linear/M\"{o}bius/cylinder
octagonal chain. In this paper, we characterized the maximum and minimum
octagonal chains with respect to the Kirchhoff index.
