The Himalayan boundary between India and Eurasia exhibits a distinct geometric form which appears to be stable over long periods of time and large deformations. This simple arcuate shape may be reproduced in a finite-element numerical model based on a thin viscous fluid sheet when the pressure across one boundary of the sheet is near-lithostatic and the boundary is allowed to deform over time. The mechanism of boundary organization in this case is analogous to that which produces round bubbles; pressures outside and inside the fluid balance and fluid in the sheet flows in such a way as to produce a constant curvature boundary. For a sheet with one lithostatic and two shearing boundaries, cuspate syntaxes also arise. This model predicts velocities within the sheet which are everywhere arc-normal as well as very high rates of syntaxial strain, two phenomena which have been observed in the Tibetan and Himalayan regions.