Numerous analyses were performed to establish the optimal shape between circular and elliptical plain cross bore at both radial and offset positions in closed thick walled cylinders. Seven cross bored cylinders with thickness ratios between 1.4 and 3.0 were studied. For effective comparison between circular and elliptical cross bores, the major radius of the elliptical cross bore was equal to that of circular cross bore. The behaviour of hoop stresses together with that of Stress Concentration Factors (SCF) were investigated at offset location ratios ranging from 0 to 0.9 using a three dimensional linear finite element analysis. Elliptical shaped cross bore predicted lower hoop stresses at radial position than circular ones, with a variation of 44.6% to 66.9% across the studied thickness ratios. With exception of K= 2.25, circular cross bores predicted lower hoops tress at 0.9 offset location ratio than elliptical ones. The minimum SCF magnitude due to circular cross bore occurred at 0.9 offset position in K=1.4, with a magnitude of 2.312. On the other hand, the lowest SCF magnitude produced by elliptical cross bore occurred at radial position with magnitude of 1.733 at thickness ratio of 2.5. This magnitude predicted by the elliptical cross bore also doubled as the overall optimum SCF in this study. For a circular cross bore, coincidence in SCF between the optimum thickness and location occurred in K=1.4 at the 0.9 offset position which also gave the best circular shape. Whereas for an elliptical shape, similar coincidence in SCF occurred respectively in K=1.75 and 2.5 at 0.685 and 0 offset positions. In conclusion, optimal location of elliptical cross bores reduce SCF magnitudes by 33% in comparison to a similar circular cross bore. However, an incorrect positioning of the same cross bore may lead to a rise of SCF magnitude by 121%.