A viscous incompressible two-fluid model with a circular cylinder under streamwise oscillations is investigated at a Reynolds number of 200 and at a displacement amplitude of A = 0.13 and for the forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f(0) = 1.25, 1.75, 2.25, 2.75. Finite volume discretization of the special integral form of two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) are performed on a fixed Cartesian grid. Improved volume-of-fluid method is used to discretize the free surface. The study focuses on the laminar asymmetric flow structure transitions in the near wake region and lock-on phenomena at a Froude number of Fr = 0.4 and for the cylinder submergence depths, h = 0.25, 0.5 and 0.75. The results detail the link between the force and the wake dynamics of the cylinder, and provide some insight into the understanding of active flow control mechanisms on coastal and offshore engineering systems. The code validations in special cases show good comparisons with previous numerical results.