The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass, which can be thought of as a simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem set up is solved by using the Frobenius method Of Solution in a power series. The developed characteristic equation is then solved numerically. The Simulation results are tabulated for a variety of non-dimensional rotational speeds, tip mass, and internal damping parameters. These are compared with the results of conventional finite element (FE) modelling as well and excellent agreement is obtained. Furthermore, it is seen that the numerical calculations according to the proposed solution method need Much less computer time as compared to the conventional FE method.