A new three-dimensional finite-element model of the steady-state dynamics of temperate glaciers has been developed and applied to Johnsons Glacier, Livingston Island, Antarctica, with the aim of determining the velocity and stress fields for the present glacier configuration. It solves the full Stokes system of differential equations without recourse to simplifications such as those involved in the shallow-ice approximation. Rather high values of the stiffness parameter B (∼0.19–0.23MPaa1/3) are needed to match the observed ice surface velocities, although these results do not differ much from those found by other authors for temperate glaciers. Best-fit values of the coefficient k in the sliding law (*2.2–2.7 x 103m a–1MPa–2) are also of the same order of magnitude as those found by other authors. The results for velocities are satisfactory, though locally there exist significant discrepancies between computed and observed ice surface velocities, particularly for the vertical ones. This could be due to failures in the sliding law (in particular, the lack of information on water pressure), the use of an artificial down-edge boundary condition and the fact that bed deformation is not considered. For the whole glacier system, the driving stress is largely balanced by the basal drag (80% of the driving stress). Longitudinal stress gradients are only important in the divide areas and near the glacier terminus, while lateral drag is only important at both sides of the terminal zone.