Heat conduction through prismatic hollow cylinders has been analyzed using a semi-analytical two-dimensional boundary collocation technique. This problem has been solved with the prior assumption of isothermal inner and outer walls. The methodology consists of using the exact solution of the governing differential equation of the problem and satisfying the given boundary conditions only at a finite number of discrete points. Based on the outcome of this method, the conduction shape factor of eccentric hollow prismatic cylinders is calculated. The position of the eccentric hole in any prismatic cylinder can lead to different orientations. Two orientations are discussed in this work. A comparison with the existing onedimensional solution to this problem is carried out and it is found that the present technique can predict more accurately than the existing one-dimensional approach.