This study investigates the behavior and capacity of concrete-filled steel tubes (CFTs) with rectangular and circular sections under various loading conditions: axial loads, pure-bending, and combined axial load-bending moments. A finite element-based numerical model is developed and validated against existing experimental data. Using an extensive databank generated from finite element analysis, this research proposes analytical empirical relations for determining the bearing capacity of rectangular and circular composite beams, columns, and beam–columns. These relations provide a direct, concise, and efficient method for calculating the ultimate strength of CFT members, making them valuable for engineering design. Comparisons between the proposed analytical results and previous experimental studies demonstrate the high accuracy of this method in analyzing rectangular and circular CFT member behavior. The findings contribute to a better understanding of CFT structural performance and offer practical tools for designers working with these composite elements.