A realistic non-spherical model for bubble formation in a co-flowing liquid is presented. In the model, an interfacial element approach is applied to describe the dynamics of bubble formation. The effect of flowing liquid velocity is modeled by a combination of the bubble axis translation and liquid pressure analysis of each interfacial element. The bubble shapes during formation are predicted reasonably well by the present model. The effects of liquid velocity, gas flow rate, nozzle radius and gas chamber volume on the bubble growth rates are studied. The model predictions are compared with the experimental data in literature and show good agreement.