Abstarct: This research investigates the vibrations of an axially accelerating viscoelastic Timoshenko beams. The beam is viscoelastic in shear which obeys The standard linear solid model and incompressible in bulk. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The governing partial-differential equations are derived from Newton’s second law. The method of multiple scales is applied to the equations to establish the solvability conditions in modal analysis¬ and principal parametric resonance.The viscoelastic beam by a parametric study, the effects of velocity, geometriy and¬ ¬viscoelastic¬ parameters investigate on the time history response, natural frequency and critical velocity.