Abstract: The unsteady flow past a circular cylinder which startstranslating and rotary oscillating impulsively from rest in a viscous fluidis investigated at Reynolds numbers Re=200 and 1000, rectilinear speedratios \alpha =0.5, 2.0 and 4.0, and for forced oscillating frequenciesf_s between 0.1 and 2.0. Numerical solutions of the Navier-Stokesequations are obtained by a finite volume method based on unstructuredcolocated meshes. The discretized schemes of the convective fluxes,diffusive fluxes and unsteadyterm are all of second-order accuracy. The SIMPLE algorithm is adopted todeal with the pressure-velocity coupling. The varieties of forcecoefficients with the control parameter are obtained after the discussion.The amplitudes of lift coefficients at natural shedding frequency and forcedoscillating frequency respectively are determined by the amplitude spectraanalysis, which show clearly the competitive relationship between the twofrequencies. Based on this relationship, the region of the classification offlow structure modes is given at last.