The distribution of basal traction on a transect along Pine Island Glacier, West Antarctica, is estimated by inverting observed surface velocities using a control method and a simple numerical stream-flow model. This model calculates the horizontal flow along a transect, based on the assumptions that the horizontal flow is independent of ice depth and that the driving stresses are balanced by resistive forces at the glacier bed and margin and by gradients in longitudinal stress. Basal traction is assumed to be linearly related to the basal velocity. For the lateral shear traction a parameterization based on an inversion of Glen's flow law is used. The application of the control method allows us to calculate the set of model parameters (e.g. the basal friction coefficient) that gives the best fit between modelled and observed surface velocities. The model is used to investigate the stress regime of Pine Island Glacier, in particular to estimate the importance of basal, lateral and longitudinal stresses relative to each other. In the flat region just behind the grounding line, basal drag, lateral drag and the longitudinal stress gradient are the same order of magnitude. In the steep region up-glacier from the grounding line, the driving stresses are highest and balanced predominantly by basal resistive stresses. Further upstream, in the trunk of the glacier, lateral and basal drag predominate.