The atomic geometry of the (2 × 1) reconstructed Si(111) surface has been determined with ion shadowing and blocking. The reconstruction involves large displacements parallel to the surface. Comparison of the experimental results with computer simulations for various reconstruction models excludes the buckling and the π-bonded molecule models, and shows consistency with the π-bonded chain model only. A structure search around the π-bonded chain model shows an optimal fit between experiment and simulations when the model includes a tilt of the upper and lower chains with respect to the surface plane. A detailed account of experimental and computational techniques is given. © 1985.