We have reconstructed the ice thickness distribution of the Morteratsch glacier complex, Switzerland, and used this to simulate its flow with a higher-order 3-D model. Ice thickness was measured along transects with a ground-penetrating radar and further extended over the entire glacier using the plastic flow assumption and a distance-weighted interpolation technique. We find a maximum ice thickness of 350+-52.5m for the central trunk of Vadret da Morteratsch, resulting from a bedrock overdeepening. The average thickness of the glacier complex is 72.2+-18.0 m, which corresponds to a total ice volume of 1.14+-0.28km3. The flow of the glacier is modelled by tuning the rate factor and the sliding parameters taking into account higher-order terms in the force balance. The observed velocities can be reproduced closely (root-mean-square error of 15.0ma–1, R2 = 0.93) by adopting a sliding factor of 12x10–16m7N–3 a–1 and a rate factor of 1.6x10–16 Pa–3 a–1. In this setting, ice deformation accounts for 70% of the surface velocity and basal sliding for the remaining 30%. The modelled velocity field reaches values up to 125ma–1, but also indicates an almost stagnant front and confluence area, which are crucial for understanding the ongoing glacier retreat.