The response and its stability of a beam rotating at nonconstant angular speed are studied. The rotating speed is assumed to be the combination of a constant angular speed and a small periodic perturbation. The axial and flexural deformations due to rotation are considered simultaneously. Thus, the rotating team at nonconstant speed yields a set of parametric excited partial differential equations of motion. Extended Galerkin’s method is employed for obtaining the discrete equations of motion. Then, the solution and the its stability are found by using the method of multiple scale.