A theoretical model is developed for modelling the non-spherical bubble formation at an orifice submerged in non-Newtonian fluids under constant flowrate conditions. The equations of motion are, respectively, the radial expansion and vertical ascension of the bubble interface, They are combined with the thermodynamic equations for the gas in the bubble and the chamber below the orifice as well as the fluid theological equation. In particular, the influence of in-line interactions between bubbles due to the fluid memory effects of the viscoelastic characteristics is taken into account for the first time. The present model is able to compute the instantaneous growing shape of the bubble during its formation and determine the final size of detachment as well as the frequency of bubble formation. The values predicted by this model compare satisfactorily with the experimental results obtained under different operating conditions.