Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic¯eld using the di®erential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural e®ect and a thickness-directed material gradient, the microbeam's behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural e®ect of the micro-scale beam is accounted for through the modi¯ed couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and°exibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to in¯nity. The magnetic¯eld is noted to have a negligibly minimal in°uence when the gradient index is lower, but a notably dominant e®ect when it is higher.