The nonlinear transverse vibrations of the rotating shaft with linear elastic supports have been analyzed. The equations are solved using the harmonic balance method to analyze the main resonances of the shaft. The mode shape of the linear beam placed on elastic supports has been used, and the partial differential equation of motion with this mode shape is converted to ordinary differential equations by the Gelerkin method. This process leads to a non-linear equation of degree 3 to obtain the beam amplitude in steady state. In all calculations, it is assumed that the shaft is in the linear elastic region. The bearings on both ends of the beam are modeled with linear springs. The coefficients of the obtained nonlinear equation are a function of the springiness of the bases. Therefore, the effect of the stiffness of the springs on the vibrations and frequency responses of the beam has been investigated. Investigations show that for shaft vibration, the nonlinear effect is of the type of stiffening spring. The relationship obtained for the natural frequency is related to the geometrical properties and the material of the shaft.