In this study, the flow and rheology of pre-collapse Larsen B ice shelf are investigated by using a combination of flow modelling and data assimilation. Observed shelf velocities from satellite interferometry are used to constrain an ice shelf model by using a data assimilation technique based on the control method. In particular, the ice rheology field and the velocities at the inland shelf boundary are simultaneously optimized to get a modelled flow and stress field that is consistent with the observed flow. The application to the Larsen B ice shelf shows that a strong weakening of the ice in the shear zones, mostly along the margins, is necessary to fit the observed shelf flow. This pattern of bands with weak ice is a very robust feature of the inversion, whereas the ice rheology within the main shelf body is found to be not well constrained. This suggests that these weak zones play a major role in the control of the flow of the Larsen B ice shelf and may be the key to understanding the observed pre-collapse thinning and acceleration of Larsen B. Regarding the sensitivity of the stress field to rheology, the consistency of the model with the observed flow seems crucial for any further analysis such as the application of fracture mechanics or perturbation model experiments.