The steady heat conduction between two parallel eccentric cylindrical walls is researched using the conformal transformation. By changing the two eccentric cylinders into two concentric cylinders, shape factors of heat conduction between two surfaces of eccentric cylinder^,s inside and outside walls, two parallel cylinders outside walls and the ground and buried pipe walls are obtained. This work should be beneficial for the calculation of heat transfer rate for correlated problems and presents a novel formulation for studies of such problems.