The first competition for a supersonic strategic heavy bomber was launched in the Soviet Union in 1967. The new plane was to have a cruise speed of over Mach 3, in response to the American XB-70 Valkyrie. It soon became apparent that such an aircraft would be too expensive and difficult to produce, so it was decided to reduce demands (in the U.S., the XB-70 project had already been cancelled).

In 1972, the Soviet Union launched a new multi-mission bomber competition to create a new supersonic, variable-geometry ("swing-wing") heavy bomber with a maximum speed of Mach 2.3, in response to the U.S. Air Force B-1 bomber project. The Tupolev design, dubbed Aircraft 160M, with a lengthened flying wing layout and incorporating some elements of the Tu-144, competed against the Myasishchev M-18 and the Sukhoi T-4 designs. Myasishchev's version, proposing a variable-geometry aircraft, was considered to be the most successful, although the Tupolev organization was regarded as having the greatest potential for completing this complex project. Consequently, Tupolev was assigned in 1973 the development of a new aircraft based on the Myasishchev design.

Although the B-1A was cancelled in 1977, work on the new Soviet bomber continued, and in the same year, the design was accepted by the government committee. The prototype was photographed by an airline passenger at a Zhukovsky Airfield in November 1981, about a month before the aircraft's first flight on 18 December 1981. Production was authorized in 1984, beginning at Kazan Aviation Association. Production of the aircraft, designated Tu-160 (factory designation "aircraft K" or "product 70"), was originally intended to total 100 aircraft, although only 35 have been produced, including three prototypes. The second prototype was lost in flight testing in 1987, the crew ejecting successfully. Production slowed due to lack of funds, and ceased in 1994, although uncompleted aircraft still remain in good condition and could be completed if orders and funding are put through.