A two-dimensional free surface flow past a circular cylinder forced to perform streamwise oscillations in the presence of an oncoming uniform flow is investigated at a Reynolds number of R=200 and fixed displacement amplitude, A=0.13, for the forcing frequency-to-natural shedding frequency ratios, f/f(0) = 1.5, 2.5, 3.5. The present two-fluid model is based on a velocity-pressure formulation of the two-dimensional continuity and unsteady Navier-Stokes equations. The continuity and Navier-Stokes equations are discretized using a finite volume approximation for two fluid regions. An improved volume-of-fluid method is employed to capture for the displacement of the free surface. The objective of this study is to examine the effects of the frequency ratios, f/f(0) = 1.5, 2.5, 3.5, and the cylinder submergence depths, h=0.25, 0.5, 0.75, on the fluid forces at a fixed Froude number of Fr=0.2. The relationship between the changes in the wake dynamics of the cylinder described in Bozkaya et al. (2011) and in the properties of fluid forces is also discussed. (C) 2015 Elsevier Ltd. All rights reserved.