The linear muffin-tin orbital (LMTO) method of bandstructure calculation has been applied to the simple tetragonal compound Cu2Sb. The d bands of Cu lie substantially below the Fermi level, and the Fermi surface is a recognizable distortion of the free-electron model. The Fermi surface has sheets in four bands. The first and second bands contain closed sheets, degenerate along a plane in the absence of spin-orbit splitting. The third band contains a multiply-connected sheet. The fourth band consists of undulating columns, degenerate along a plane with the third band in the absence of spin-orbit splitting, and of another closed sheet. Earlier de Haas-van Alphen results are explained semiquantitatively by the model, which also accounts for open orbits seen in high-field magnetoresistance experiments.