The Matra MS640’s design incorporated a tubular trellis frame, similar to the MS650. Robert Choulet, an aerodynamic engineer previously with Deutsch & Bonnet, designed the car’s coupe bodywork. Choulet’s design was characterized by a drop-shaped body, an extremely elongated shape, a small cockpit covered by a bubble roof, rounded wheel arches, and stabilizing fins on the tail. The car’s appearance was described as record car-like.
Following the performance of the Matra MS630 in 1968, Matra director Jean Luc Lagardère tasked Robert Choulet with designing a closed car specifically for the Circuit de la Sarthe. The goal was to address the power disadvantage Matra faced against Porsche and Ford, and also to reduce fuel consumption. The resulting car generated significant anticipation, with hopes of a French victory at the 24 Hours of Le Mans.
At collective tests in March, the MS640 was not yet ready, and only the MS630 was fielded. A private test session was then organized in April at the Circuit de la Sarthe with Henri Pescarolo and Johnny Servoz-Gavin at the wheel. Pescarolo was the first to drive, instructed to gradually push the car to its limits. While reaching 250 km/h (160 mph) on the Hunaudières straight, the car took off after hitting a bump, flipped, and crashed. Pescarolo sustained burns, fractures, and spinal injuries, requiring six months of convalescence. He later won the 1000 km of Paris aboard a Matra 650 paired with Beltoise. Lagardère declined to fund a second MS640, leading Choulet to leave Matra in October 1969 for the Société d'Études et de Réalisations Automobiles (SERA-CD) and work on the Porsche 917.
Following the accident, investigations suggested that bending in the upper part of the doors under aerodynamic pressure caused the instability. Choulet believed that gradually reaching the car’s maximum performance would have revealed the issue.
The original molds for the MS640 were discovered in the Matra factory in 1989, along with some parts of a second bodywork. In 1995, Norma built a second frame and recreated the missing bodywork parts based on the original designs. Reconstruction stalled for nine years due to a lack of skilled craftsmen, but was completed by EPAF in 2004.
Upon completion, the rebuilt car was tested with Henri Pescarolo, who requested to drive to complete the work interrupted decades earlier. To prevent a repeat of the 1969 accident, the car was equipped with a sensor system to warn the driver of impending lift-off. Despite modifications and adjustments, the car reached almost 290 km/h (180 mph) without taking off. However, overheating of the rear brakes, caused by deactivating the front brakes, resulted in a small fire during the test. Pescarolo, satisfied with the outcome, completed the test despite the fire.
The Matra MS640 was exhibited at the Espace automobiles Matra museum in Romorantin – Lanthenay, France, and was offered for auction by Bonhams in Paris on February 6, 2025.