The present work examines numerically the deformation and breakup of free falling droplets subjected to a continuous Cross flow. The model is based on the solution of the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology utilized for tracking the droplet-air interface; an adaptive local grid refinement is implemented in order to decrease the required computational cost. Neglecting initially the effect of the vertical droplet motion, a 2D axisymmetric approximation is adopted to shed light on influential numerical parameters. Following that, 3D simulations are performed which include inertial, surface and gravitational forces. The model performance is assessed by comparing the results against published experimental data for the bag breakup and the sheet thinning breakup regimes. Furthermore, a parametric study reveals the model capabilities for a wider range of Weber numbers. It is proved that the model is capable of capturing qualitatively the breakup process, while the numerical parameters that best predict the experimental data are identified. (C) 2016 Elsevier Ltd. All rights reserved.