Under the simply supported boundary conditions, the natural frequencies and modal functions of transversally nonlinear free vibrations of axially moving beams were approximately analyzed in the supercritical regime. Complex modal analysis method was devoted to the governing equation, an integropartialdifferential equation.Galerkin method was applied for the linear standard equation, an ordinary differential equation with a spatially dependent coefficient. The effects of different truncations on natural frequencies were shown. Based on the 8term Galerkin truncation, the effects of system parameters on modal functions were discussed.