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This study develops a finite element solution to analyze the vibration response of multi-layer shape memory alloy (SMA) composite beams. Using Euler–Bernoulli beam motion equations with tension–compression asymmetry, based on Poorasadion’s model, the Newmark method and Newton–Raphson technique are employed. Validating the model against ABAQUS/Standard results for a homogeneous SMA beam shows good agreement. This research explores the dynamic characteristics of bi-layer and tri-layer SMA beams, presenting deflection–time, stress–strain, and velocity–deflection profiles. SMAs’ hysteresis property effectively reduces early-stage vibration amplitudes, and their energy-dissipating feature during phase transformations makes them promising for controlling dynamic performance in engineering applications.