The project began in June 1981, and the first prototype chassis was completed on March 27, 1982, in time for the beginning of the World Championship season.

The 956 features a chassis made of an aluminium monocoque, a first for the company, helping to allow the car to meet the 800 kg (1,764 lb) weight minimum in Group C. The engine is the same as the one used in the Porsche 936/81, the Type-935 2.65 L turbocharged Flat-6, producing approximately 635 hp (474 kW) (originally developed as an Indycar engine; hence the cubic capacity used).

The engine became highly successful in F1, and while never the most powerful on the grid, between 1984 and 1987, the turbocharged TAG-Porsche would win 25 Grands Prix and help McLaren to two Constructors and three World Driver's Championships.

The 956 made its debut at the Silverstone 6 Hour race, the second round of the World Championship for Makes with Jacky Ickx and Derek Bell driving for the factory.

After missing the following round at the 1000 km Nürburgring for developmental reasons, the Ickx/Bell unit reappeared at the 24 Hours of Le Mans.

The overall all-time lap record for the demanding 20 km Nürburgring-Nordschleife circuit in the Eifel Mountains was achieved during the qualifying session for the 1983 1000km of Nürburgring, by Stefan Bellof, who drove his 956 around in 6 minutes 11.13 seconds, at an average speed of 202 km/h (126 mph).

At the 1985 1000 km of Spa, Bellof died after his Brun Motorsport's 956 collided with the factory team's newer 962 that being driven by Jacky Ickx.