The present work reports a numerical investigation of the flow past an oscillatory square cylinder at Re = 100. A fixed finite element immersed technique is proposed to solve the incompressible fluid-rigid body interaction problem. The study encompasses the analyses of the flow over a fixed cylinder and transverse to the flow and streamwise oscillating cylinders. The dimensionless frequency f(r), i.e., the ratio between cylinder's oscillation and Strouhal frequencies, and motion amplitude are used to characterize the flow pattern evolution and its action on the cylinder. First, to compute the flow over the cylinder, a mesh size is determined from a mesh sensitivity analysis where the drag and lift coefficients computed using the immersed method are compared with those obtained from a body-fitted mesh. A reasonable numerical convergence is found from such analyses. Second, the oscillating square cylinder cases are studied to describe the synchronization regions. To this end, an oscillating body motion is prescribed varying the frequency of the imposed displacement with a constant amplitude. The synchronization zones are determined when the aerodynamic coefficients exhibit the most significant variations. In particular, the lock-in phenomenon is observed at f(r) approximate to 1 for transversely oscillating square cylinders, confirming some aspects previously reported in the literature using other numerical techniques. In the present work, lock-in is determined at f(r) approximate to 2 for streamwise oscillating square cylinders, results is not longer found in the literature. (C) 2018 Elsevier Masson SAS. All rights reserved.