<p>Piezoelectric devices are often integrated with elastic substrates to ensure their structural reliability and performance. To model the interaction between piezoelectric devices and their substrates, the elastic foundation model is commonly adopted. However, many of these models overlook the significant influence of foundation inertia, which can substantially affect the system’s dynamic response. This paper proposes a theoretical model that accounts for the substrate mass, aiming to investigate its influence on the free vibration and static bending of functionally graded piezoelectric beams resting on elastic foundations. Based on electro-elasticity theory and the elastic foundation model, a state-space method is applied to derive the governing equations for functionally graded piezoelectric beams with material properties that vary continuously through the thickness. The differential quadrature method is further adopted to analyze the natural frequency and bending responses under various boundary conditions. Numerical results reveal that foundation parameters significantly influence the natural frequencies, bending deformation, and electric potential distribution of the beams. It is noted that the beam’s dynamic behavior is highly sensitive to the foundation mass. These findings provide valuable insights for the design and optimization of advanced piezoelectric structures.</p>