Proton Exchange Membrane Fuel Cell performance significantly depends on electrode water content. Indeed, an excess of liquid water in the pores of the gas diffusion layer (GDL) and in the gas flow channel (GFC) can drastically bring down the output power. Depending on the operating conditions, liquid water emerging from the GDL micro-channels can form droplets, films or slugs in the GFC. In the regime of droplets formation, the interaction with the gas crossing-flow leads to an oscillating mechanisms that is fundamental to studying the detachment from the GDL surface, as the authors have shown in a previous publication. In this work, a numerical model of a droplet growing on the GDL surface is developed to describe the interaction between droplet cross-flowing gas stream. The droplet shape and its deformation are reconstructed assuming a known geometry. Therefore, a lumped force balance is enforced to determine the center of mass motion law. Oscillation frequencies during growth and at detachment are found as a function of droplet size. The model is also exploited to find the relationship between droplet critical detachment size and gas velocity. The numerical results are compared with the droplet frequency-size and detachment size-gas velocity experimental results previously presented by the authors. The matching between the numerical and experimental data is very good and is a mean of validation for the model. The low computational burden and the conciseness of the results make the model suitable for applications such as control and optimization strategies development to enhance PEMFC performance. Additionally, the model can be exploited to implement monitoring and diagnostic algorithm.