STS-76 was NASA's 76th Space Shuttle mission, and the 16th mission for Atlantis. STS-76 launched on 22 March 1996 at 3:13 am EST(UTC-5) from Kenndy Space Centre launch pad 39B. STS-76 lasted over 9 days, traveled about 3,800,000 miles (6,100,000 km) while orbiting Earth an estimated 145 times, and landing at 5:28 am PST (UTC-8) on 31 March 1996 at Edwards Air Force Base runway 22.

The flight was the third Shuttle mission to dock with the Russian Space Station - Mir, as part of the Shuttle-Mir programme, carrying astronaut Shanon Lucid to the orbital laboratory to replace NASA astronaut Norm Thagard. STS-76 also carried a SPACEHAB single module along with Lucid, and on flight day 6 Linda Godwin and Michael R. Clifford performed the first U.S.spacewalk around two docked spacecraft

The mission was the third linkup between a U.S. Space Shuttle and Russian space station Mir, and brought veteran astronaut Shannon Lucid to Mir to become the first American woman to live on the station. Her approximately four-and-a-half-month stay also eclipsed the long-duration U.S. spaceflight record set by the first American to live on Mir, Norm Thagard. Lucid was succeeded by astronaut John Blaha during STS-79 in August, giving her the distinction of membership in four different flight crews—two U.S. and two Russian—and her stay on Mir kicked off the continuous U.S. presence in space for the next two years.

Payload bay configuration included the Orbiter Docking System in the forward area and a SPACEHAB single module toward the aft. STS-76 marked the first flight of a SPACEHAB pressurized module to support Shuttle-Mir dockings. The single module primarily served as a stowage area for a large supply of equipment for transfer to space station, but also carried the European Space Agency's Biorack experiment rack for on-orbit research.

Atlantis hooked up with Mir on flight day three, following same R-bar approach employed on STS-74. Actual connection between Orbiter Docking System and the Kristall module's docking port occurred at 9:34 pm EST, 24 March. Hatches opened a little less than two hours later. Awaiting Atlantis' arrival were Mir 21 Commander Yuri Onufrienko and Flight Engineer Yuri Usachev, who were launched to Mir on 21 February. In July, they were joined by Mir 22 Commander Valeri Korzun, Flight Engineer Alexander Kaleri and CNES astronaut Claudie Andre-Deshays. After a two-week stay, Andre-Deshays would return to Earth with Onufrienko and Usachev while Korzun and Kaleri remained on board with Lucid.

During five days of docked operations, about 1,500 pounds (680 kilograms) of water and two tons of scientific equipment, logistical material and resupply items were transferred to Mir. Experiment samples and miscellaneous equipment brought over to orbiter. In Biorack, 11 separate scientific investigations were conducted. Study topics included the effect of microgravity and cosmic radiation on plants, tissues, cells, bacteria and insects, and the effects of microgravity on bone loss. Also transferred to the station were Mir Glovebox Stowage (MGBX) equipment to replenish glovebox already on station; Queen's University Experiment in Liquid Diffusion (QUELD) flown in orbiter middeck locker; and the High Temperature Liquid Phase Sintering (LPS) experiment.

On flight day six, Godwin and Clifford conducted what some claim to be the first U.S. extravehicular activity (EVA) around two mated spacecraft. However, this appears to ignore the Apollo 9 EVA, and EVAs during Skylab. During six-hour, two-minute, 28-second EVA, they attached four Mir Environmental Effects Payload (MEEP) experiments to the station's docking module - designed to characterize the environment around Mir over an 18-month period. Godwin and Clifford wore Simplified Aid For EVA Rescue (SAFER) propulsive devices - first flight-tested during STS-64.

Other payloads included Shuttle Amateur Radio Experiment (SAREX); KidSat, a project that gives middle school students opportunity to participate in space exploration; and Trapped Ions in Space (TRIS), a Naval Research Laboratory experiment flown in a Get Away Special canister in the payload bay.