Using analytical and numerical techniques, a two-dimensional (2-D) map-plane model and a 2-D flowline model are utilized to elucidate the horizontal and vertical ice deformation at the confluence of two glaciers. For a perfectly symmetrical confluence, the junction point of the two tributaries can be modeled as a no-slip/free-slip transition. A strongly localized surface depression develops around the junction point, accompanied by two broadly elevated zones positioned close to the margins of the tributaries facing the junction point. The confluence center line is subjected to horizontal longitudinal extension and a transverse compression. The compression generally exceeds the concomitant longitudinal extension in magnitude. Depth-integrated vertical strain rates along the center line are positive (extension), but the strain-rate variation with depth depends critically on the type of basal boundary conditions at the glacier bed. For a no-slip boundary condition, vertical strain rates change from positive at the surface to negative close to the base, whereas for a free-slip boundary condition (perfect sliding) vertical strain rates are positive throughout the depth. These theoretical results are compared with field measurements from Unteraargletscher, Bernese Alps, Switzerland.