Metal-Ceramic Functionally Graded Materials (FGM) find extensive applications in nuclear power generators, spacecraft systems, and energy conversion systems. This study aims to investigate the behavior of FGMs under transient thermal loads and time-dependent mechanical loads through finite element modeling. A 2D model is developed using COMSOL Multiphysics to simulate the behavior of a metal-ceramic FGM thick cylinder. The model considers Titanium-Zirconium-Molybdenum (TZM) alloy for metals and Silicon carbide (SiC) for ceramic. It accounts for the effects of transient thermal loads and internal time-dependent pressure exerted on the cylinder's inner surface. Thermo-mechanical properties, assumed to follow an exponential function, are incorporated into the model. Numerical analysis results are compared with established analytical solutions to validate the model. Graphical comparisons between numerical and analytical results demonstrate significant agreement, confirming the reliability of the numerical approach. This study provides insights into the behavior of metal-ceramic FGMs under transient thermal and mechanical loads. The findings underscore the effectiveness of finite element modeling in understanding complex interactions within FGMs. Future research directions include exploring more complex geometrical models, incorporating additional loading scenarios, and performing experimental validation to enhance understanding of FGM performance in real-world conditions.