This report examines how changing the content of the functionally graded material (FGM) core affects the unctionally graded sandwich (FGSW) beams' stability. The study uses Hamilton's principle with finite element analyses to formulate the problem, and Floquet's theory to establish the stability boundaries. The FGSW beam's material properties can be described by either a power law with varying indices or an exponential law. The investigation finds that increasing the FGM content shifts the instability regions closer to the dynamic load factor axis, making the beam more susceptible to dynamic instability for FGSW-2.5 beams. However, the effect is opposite for e-FGSW beams. These findings suggest that engineers and designers need to consider the FGM core content when designing FGSW beams for optimal stability. By understanding the impact of FGM content, they can create more stable and reliable structures.