<p>This study investigates the intricate size-dependent electromechanical buckling behavior of composite nanobeams featuring a perforated functionally graded core and piezoelectric layers on an elastic foundation. Employing the nonlocal strain gradient theory, which integrates both piezoelectric and flexoelectric effects, governing equations are derived for Euler–Bernoulli and Timoshenko beam models. The core’s functionally graded material properties are assumed to vary continuously along the thickness direction, following a power-law distribution. Furthermore, closed-form expressions for the geometrical variables of the perforated core are developed. Analytical solutions for the electromechanical critical buckling loads are derived and rigorously validated against the established literature. Numerical simulations reveal the profound influence of material gradation, perforation geometry, and the interplay of nonlocal and flexoelectric effects on the buckling characteristics of these nanostructures. Key findings indicate that increasing the gradation index (<i>n</i>) from 0 to 14 leads to a significant reduction in the critical buckling load parameter. Specifically, a 31.44% decrease is observed for Timoshenko nonclassical electromechanical behavior at a filling ratio (<i>α</i>) of 0.75, and a 72.07% decrease for classical mechanical behavior at <i>α</i> = 0.5. Moreover, enhancing the normalized shear component of the elastic foundation parameter (<i>Κ</i>_<i>p</i>) from 0 to 2.5 results in a dramatic increase in the Timoshenko nonclassical mechanical critical buckling load by 1167.07% at <i>n</i> = 0, which reduces to 1087.06% at <i>n</i> = 2. These insights provide a valuable foundation for optimizing the design and performance of advanced nanoelectromechanical systems (NEMS).</p>