This study presents a dynamic modeling framework for analyzing the forced vibration of multidirectionally functionally graded viscoelastic beams (MDFGVBs) under moving loads and varied boundary conditions. The formulation incorporates three-dimensional material gradation along axial, transverse, and thickness directions with Kelvin–Voigt viscoelastic damping. Governing equations are derived using Euler Bernoulli and Timoshenko theories to capture bending, shear deformation, and rotary inertia. A hybrid Ritz–Newmark method ensures accuracy and stability. Validation confirms reliability, while parametric studies reveal damping-induced deflection reduction, resonance shifts, and nonlinear gradation effects, offering high-fidelity predictions for advanced structural applications in aerospace, mechanical, automotive, and civil engineering.