M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / The purpose of this research was to develop optimal numerical solutions that can be employed during the design of cross bored thick-walled compound cylinders. The geometric design parameters of a cross bored compound cylinder that were optimized include shrinkage pressure, cross bore size, shape, location, and obliquity. Finite Element Analysis (FEA) modeling software called Abaqus version 2019 was used to generate numerical solutions. A total of 48 different part models were created and analyzed in this work. The generated FEA results from these models were validated using analytical solutions developed from Lame’s theory. The effects of shrinkage pressure on hoop stresses and Stress Concentration Factor (SCF) were studied to determine the optimal conditions. The optimum shrinkage pressure obtained was henceforth used for further analysis in this work. In addition, using one factor at time optimization technique, an optimization process was carried out to determine the optimal combination of the cross bore configuration geometry that gives minimum SCF. These parameters of cross bore configuration geometry include different sizes of either circular or elliptical-shaped cross bore, positioned at radial, offset, and/or inclined. The analyses of the effects of shrinkage pressure ranging from 4.4733 to 223.662 MPa on 11 different part models, established that the shrinkage pressure of 89.464 MPa generated the minimum SCF magnitude of 3.02. After analyzing 8 different circular cross bore size ratios ranging from 0.1 to 0.8, at the radial position, it was established that the hoop stress increases with an increase in a cross bore size. The smallest cross bore size ratio of 0.1 gave the lowest hoop stress and minimum SCF of 3.02. Whereas the highest stress was developed at the cross-size ratio of 0.8 with an SCF magnitude of 6.75. The minimum magnitude of SCF translates to a reduction of the pressure carrying capacity of the compound cylinder by 67% than a similar plain compound cylinder. Generally, offsetting of the circularly shaped cross bore from the radial position, led to a reduction of the magnitude of SCFs. For instance, from the 8 offset positions analyzed, the minimum SCF occurred at the offset position of 0.006 m with a magnitude of 2.50. This SCF magnitude indicated a reduction of pressure carrying capacity of 60% in comparison to a similar plain compound cylinder. Evaluation of 12 different diameter ratios of elliptical-shaped cross bore ranging from 0.5 to 10, at the radial position, established the lowest SCF magnitude of 1.33 that occurred at a diameter ratio of 5. Henceforth, this optimum diameter ratio was used for further analysis. This aforesaid SCF magnitude translated to a reduction of the pressure carrying capacity of the compound cylinder by 24.81% when compared to a similar plain compound cylinder. Besides, offsetting of elliptically shaped cross bore generally decreased the magnitudes of SCFs. Therefore, for elliptically shaped cross bore, the lowest SCF occurred at radial position with magnitude of 1.33. A general comparison between the effects of circular and elliptical cross bore, established that the elliptical-shaped cross bores generated both lower hoop stresses and SCFs than those of circularly shaped cross bores. On the other hand, oblique elliptical offset cross bores along the Z-axis of the compound cylinder led to an increase in SCFs. As the oblique angle increased from 0 0 to 75 0, the SCFs also increased progressively, however, there was a significant increase in SCF when the inclination angle increased from 60 0 to 75 0. The lowest and highest SCF magnitude was 1.52 and 1.92 at 15 0 and 6.19 at 75 0, respectively. Overall, the optimum geometric configuration of a cross bore in a thick compound cylinder was found to be elliptically shaped, offset at radial position which is an obliquity angle of 0 0 having a diameter ratio a/b of 5.