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.