Summary: Employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, and then utilizing the reductive perturbation technique, we examine the amplitude modulation of weakly nonlinear waves. It is shown that the amplitude modulation is governed by a nonlinear Schrödinger equation. The result is compared with some previous works on the same subject. The modulation instability of the monochromatic wave solution is discussed for some elastic materials and initial deformation.