Thin-wall structures, particularly thin-walled tubes, play a critical role in load-bearing structures. Enhancing their ability to withstand crushing loads can significantly improve the overall damping efficiency of the system. Functionally graded thickness (FGT) is a promising approach for enhancing the load-bearing properties of thin-walled tubes by enabling control over material usage and localized deformation patterns within the structure. In this study, we proposed a novel theoretical model that analyzes the crushing behavior of hollow and foam-filled FGT thin-walled circular tubes by considering four primary failure mechanisms that contribute to energy dissipation: (1) bending of plastic hinges, (2) membrane stretching, (3) axial foam crushing, and (4) the interaction between foam and the tube's wall. We validated our model against experimental results from previous researchers and observed a good agreement. Additionally, we conduct a comprehensive study to examine the effects of various geometrical parameters, such as power-law functions and normalized wall thickness ratio, on the crushing behavior of FGT structures. Our results demonstrate the accuracy and reliability of our theoretical model and highlight the potential of FGT structures to enhance the performance of thin-walled tubes in a range of load-bearing applications.