Abstract: The unified differential equation of buckling and motion of viscoelastic beams under uniformly distributed follower forces in time domain is established by differential operators. The equation has extensive applicability and is suitable for various viscoelastic models. The governing equation of a three-parameter viscoelastic model is obtained. The dynamic descretization equation(complex eigenvalue)of viscoelastic beams of three-parameter model under follower forces is derived by power series method. Boundary conditions such as simply-simply, clamped-clamped and simply-clamped ends are considered. The curves of negative real part(decaying coefficient)and imaginary part(decaying vibration frequency)versus uniformly distributed follower forces are obtained using quasi-Newton method.