Numerous plate theories have been developed to efficiently address diverse plate-related challenges. Within this realm, a family of five-variable plate theories, whose displcements are characterized by the form given in Eq. (1), has found applications in static and dynamic analyses of intact laminated composite plates and functionally graded material (FGM) sandwich plates. Various functions of f(z) have been introduced to portray shear strains along the thickness direction, uniformly resulting in zero shear strains on a plate's top and bottom surfaces. This study pursues two primary objectives. Firstly, it proposes a well-suited set of basis functions to establish admissible functions through the moving-least-square technique for accurate vibration analyses of a side-cracked FGM plate via the Ritz method. This set incorporates crack functions extracted from the asymptotic solution for stresses at a crack tip in an FGM plate, adeptly capturing discontinuities in displacements and slopes across the crack. The second objective involves an exploration of the impact of different functions of f(z) on the natural frequencies of FGM rectangular plates exhibiting various combinations of boundary conditions and featuring side cracks with diverse configurations. Consider a simply supported Al/AL2O3 FGM square plate with a thickness-to-length ratio (h/a) of 0.2, housing a vertical central side crack with a crack length equal to 0.5a. Table 1 displays the well-converged nondimensional frequencies of the plate with an increasing number of admissible functions. The obtained results closely align with published outcomes based on three-dimensional elasticity theory. Table 2 reveals that the four functions of f(z) proposed in the literature insignificantly influence the frequencies of a side-cracked FGM plate.