Coil-wound heat exchanger, which has a large-scale turbulence in the shell side and a great heat transfer coefficient, has been widely used in chemical industry, such as liquefied natural gas (LNG) and crude pyrolysis of ethylbenzene. To investigate the general vibration characteristics, a complete wound tube can be divided into the curved tube and the coil tube for easy research because of its constraint condition. A finite element analysis is used to obtain the natural frequencies and corresponding mode shapes of the curved tubes and the coil tubes with various parameters. For the curved tube, the deformation of middle position of the tube is larger than that of the clamped ends. The maximum deformation occurs at the transition from the bending tube to the straight tube. With the increase of R1 and the decrease of R2, H1, H and θ, the natural frequencies of curved tube increase which is more likely to avoid the fluid-elastic instability, in which R1 is circumferential radius of the straight part of curved tube, R2 is coil radius, H1 is axial straight tube length, H is axial height of curved tube and θ is deflection angle. And for the coil tube, all the deformation for mode shape occurs in the axial direction, and there is no obvious deformation in the radial direction. With the increase of support number and the decrease of R2, the basic frequency of the coil tube increases. It provides a certain reference for the support layout of coil-wound heat exchanger.