Abstract <p>Transverse vibration eigenfrequencies of functionally graded beams carrying supplementary point masses are computed aided by the scaled boundary finite element method (SBFEM) coupled with the precise integration approach (PIA). Instead of traditional inhomogeneous beams graded along the thickness, material gradations investigated in this paper are expressed as arbitrary mathematical formula regarding the lengthwise <i>x</i>-axis. Furthermore, additional concentrated masses are attached to any positions of the beam. Only the longitudinal axis is requisite to be meshed on the basis of high order spectral elements. Each node of the discretized element possesses only two degrees of freedom comprised by the displacement field across <i>x</i> and <i>z</i> axes. Making use of the introduced scaled boundary coordinate system <i>z</i>–η and the dual vector methodology, the first order ordinary differential governing matrix equation of the axially functionally graded beam is exhibited. The governing equation is calculated by the PIA to furnish highly accurate stiffness matrix. Implementing the same degrees of freedom matching integrates added masses and the mass matrix of the nonhomogeneous beam. Depended upon the stiffness and mass matrices, natural frequencies of functionally graded beams with extra masses are revealed. Excellent agreements between present solutions and reference results are achieved to portray high precision of the suggested technology. Subsequently, influences of several parameters, such as boundary constraints, gradient factors and number of auxiliary masses, on modal characteristics of axially functionally graded beams are exposed.</p>