The　nonlinear　vibrations　are　investigated　for　a　pipe　conveying　fluid　on　simple　supports,　where　the　supporting　boundaries　are　exerted　by　harmonic　vibrations　of　displacement.　For　a　pipe　constituted　by　the　Kelvin　model,　the　effects　of　the　viscoelasticity,　the　nonlinearity,　the　mass　ratio　of　the　pipe　and　the　fluid　are　analyzed　via　the　method　of　multiple　scales.　Numerical　examples　are　presented　to　show　the　steady-state　response　of　the　pipe　on　the　amplitude-frequency　plane.