A non-spherical model for bubble formation at an orifice with liquid cross-flow has been developed. The interface element approach is applied to describe the dynamics of bubble formation. The effect of liquid cross-flow on the bubble formation process is modelled by a combination of tilting of the bubble axis and liquid pressure analysis of each element on the bubble interface. Model predictions compare well with the experimental results available in the literature for different conditions of gas flow rate, orifice diameter and liquid cross-flow velocity. Simulated bubble shapes are highly non-spherical, especially at high liquid velocities, and bear a striking resemblance with the experimental high-speed video sequences.