The basic principles of the architecture of many viral protein shells have been successfully established from electron microscopy and X-ray data^1–4, but enveloped viruses have been more difficult to study because they resist crystallization and are easily deformed when prepared for electron microscopy. To avoid the limitations of conventional techniques when applied to enveloped viruses, we have used a cryo-electron microscopy method in which unfixed and unstained viruses are observed in an unsupported thin layer of vitrified suspension^5,6. Because of electron beam damage, the many different views required for high-resolution three-dimensional reconstruction cannot be obtained from a tilt series of the same particle. The images of many differently oriented viruses are combined using a novel reconstruction method, ‘reconstruction by optimized series expansion’ (ROSE)⁷. The structure of the envelope of Semliki Forest virus has been reconstructed to 3.5-nm resolution. The T = 4 geometry of the surface lattice, the shape of the trimeric spikes and their arrangement on the lipid bilayer are visualized.