First, a uniform viscous and incompressible flow past a circular cylinder was simulated by using the Ansys/Flotran CFD software, then the induced vibration for a viscous flow past a circular cylinder supported by elastic spring and dash pot was simulated with the Ansys/Flotran CFD software and stepwise integration. The lift forces and transverse responses were analyzed with the fast fourier transform(FFT). By analyzing the calculation results, some useful conclusions were given, which may be used in the designing of equipments with viscous flow past a circular cylinder supported by elastic spring and dashpot.