[en] The flow induced motion (FIM) of an elastically mounted trapezoid cylinder with different body shapes is numerically studied by solving two-dimensional unsteady Reynolds-averaged Navier–Stokes equations. The trapezoid cylinder is mounted on end-supporting linear springs constrained to oscillate normal to the direction of flow and the axis of cylinder. Numerical simulations were performed in Reynolds number(Re) range from 10 000 to 120 000. The ratio of the rear and front edge width of the cylinder, λ, varies from zero to one. Both vortex-induced vibrations (VIV) and galloping are observed for the cylinder in the tested cases. The VIV upper branch for trapezoid cylinder with λ = 0.8 and square cylinder (λ = 1) are clearly observed in the amplitude and frequency responses. Galloping are exhibited for trapezoid cylinder with different body shapes when Re ≥ 90 000. The FIM responses of the square cylinder is obviously weaker than the triangle and trapezoid cylinders, since the interaction between the separated shear layers on the upper and lower sides of the cylinder becomes weak as λ increases. The maximum value of amplitude is achieved at 4.51D (D is the front edge width of the trapezoid cylinder) for λ = 0.6 at ${U^{\ast <!--\; ???\; -->}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$ = 22.21 (Re = 120 000), where ${U^{\ast <!--\; ???\; -->}}_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$ = U/(f _n,water D) and f _n,water is the natural frequency of the oscillatory system in water. Up to 18 vortices are observed in the galloping branch. The displacement trend of the cylinder matches well with the lift forces, especially in the galloping branch. (paper)