In the previous report, the author has given an analytical study of two elastic annular plates, which are placed concentrically in parallel each other, and which are interconnected each other by a number of elastic rods. These elastic rods were assumed to be arranged in a single row along a concentrical circle. The present paper in the outcome of continuation of the author's previous study, and gives the result of analytical study about the case in which two rows of rods are arranged along two different (but concentric) circles. Results of this analytical study were evaluated numerically for the case of the number of rods along each circular orbits are, N=6, 12, and 18. The rods (as done in the previous report) assumed to suffer a thermal expansion probably due to the external heating. The two (top and bottom) annular elastic plates are assumed to be of different thickness. The author's intention is to supply some suggestion in connection with the structural design of once-through boilers and also of guide-rings of hydraulic turbines. The results of numerical evaluation are shown as graphs.