<p>The free vibration behavior of beams with both variable cross-sectional geometry and material inhomogeneity along the beam axial direction is studied. The finite element method is employed to analyze the influence of cross-sectional variations on the dynamic characteristics of beams with polynomially graded material properties along the beam length. Both one- and three-dimensional finite elements are developed incorporating axial material gradients via user-defined material subroutines (UMAT) in ABAQUS package. The free vibration analysis is performed using both finite element models to determine natural frequencies and mode shapes across a wide range of tapered beam configurations. The accuracy and efficiency of the models are validated by comparing the numerical results with data available in the literature. The findings reveal that variations in cross-sectional geometry have a significant impact on the natural frequencies highlighting their critical role in the dynamic response of axially inhomogeneous tapered beams.</p>