<p>This paper presents an analytical investigation into the dynamic behavior of bidirectional functionally graded (BDFG) Rayleigh nanobeams subjected to an external magnetic field along the longitudinal direction. Eringen’s nonlocal elasticity theory captured the size effects while two material parameters control the material properties due to blending of two materials along the length and thickness directions. The longitudinal magnetic field effects are captured by the Lorentz force. The governing equations, which account for material gradations, magnetic and nonlocal effects, are derived by using Hamilton’s principle. Laplace transform method is employed to solve the governing equations analytically. Natural frequencies of the nanobeam are determined for various support conditions, including simply supported, clamped, and cantilever nanobeams. Results show that the magnetic field increases the beam’s natural frequencies, while the material gradations allow for precise tuning of the beam’s mechanical properties, which in turn, affect the natural frequencies. This comprehensive analysis provides insights into optimizing the dynamic properties of BDFG nanobeams, with potential applications in fields such as aerospace, micro-electromechanical systems (MEMS), and nanotechnology.</p>