This paper theoretically investigatied the geometrically nonlinear free vibrations of a simply supported beam containing an open crack under large vibration amplitudes, and established a semianalytical solution about the beam of nonlinear vibrations. Using the combined mode functions of line model to express the mode functions based on the Rayleigh method, the first mode explicit expression of nonlinear vibrations was established. The effects of various crack depth and the assigned different first function contribution a1 on the maximum displacements of the crack beam were numerically simulationed. An explicit solution is simple and ready to use for engineering applications.