The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to their wide applications in physics and chemistry. These indices have been computed for many interesting graphs, such as linear polyomino chain, linear / Möbius / cylinder hexagonal chain, and linear octagonal chain. In the present paper, we consider Möbius octagonal chain (Mn) and cylinder octagonal chain (M’n). Explicit closed-form formulae of the Kirchhoff index and the number of spanning trees are obtained for Mn and M’n.