This study presents results concerning the vibrational characteristics of a mild steel and carbon/epoxy composite hollow shaft system under different boundary conditions. Finite element analysis has been deployed for critical investigation. The effect of cutout profile and its geometric location over natural frequency and mode shape is studied in detail. From the results, it is clear that the introduction and increase in the number of cutouts leads to a drastic reduction in the natural frequency of the system for both the cases. Moreover, the geometric location of cutouts has a predominant effect in deciding natural frequencies and corresponding mode shapes. The results presented in this study will yield higher levels of interest for engineers dealing with topology optimization problems, where material removal is inevitable.