The M1B was the McLaren team car for 1965 through to 1996, as well as the McLaren Elva customer car for 1966. Elva announced they would be building the M1B in September 1965. It was the second car to be produced by Elva, but the first to be successful for both works and customer drivers, in England and America. Elva produced 28 M1Bs.

The design was based on the M1A, with engineer Robin Herd retaining and revising the frame to make it 20% stronger without gaining any weight. The strength was gained by using larger diameter round and square mild steel tubes stiffened by sheet alloy riveted and bonded to it, forming the undertrays and bulkheads. The M1B body was designed by English motorsport artist Michael Turner. He also created the Team McLaren badge, using an image of the Kiwi, the iconic New Zealand flightless bird. Turner designed the M1B body using very strict guidelines laid down by Bruce, including a rigid set of cross sections and aerodynamic requirements. After the final drawings were made, a model was built for wind tunnel testing to improve lines and streamlining. Much attention was paid to the lift and drag characteristics. The M1B's front end was blunt, shaped like the Penske Zerex, to eliminate the uplift that had been apparent with the more wing-shaped M1A. A clear plexiglass spoiler was also added to the rear of the M1B to help with downforce.

The M1B in the Mathews Collection is 12 of the 28 produced. Peter Revson ran this M1B equipped with a Ford engine at the sports car supporting race for the British GP at Brands Hatch 1966. It is one of a pair bought by American Bill Kay for himself and Revson to run. Unfortunately, Kay suffered a fatal heart attack before the GP and his cars were taken over by George Drummond, who took them to the Can-Am championship. Later that season, in Nassau for the Bahamas Speed Week and with the Drummond M1B Ford, Revson had a good race leading for most of the way before his brakes failed, but he had completed enough of the circuit to be awarded third. In Las Vegas for the last race of the 1966 Can-Am series, Revson started ninth on the grid and finished an impressive fourth. In 1967, the M1B was bought by Skip Barber who raced it establishing a new record at Lime Rock. Barber ran the M1B in the first three races of 1967 Can-Am series. His best starting position was fifteenth at Elkhart Lake on September 3 and his best finish was seventh in the same race.

Although this chassis has had a long and hard racing life, when the car was acquired early in 2000 for the Mathews Collection, it was still in amazingly original condition, and with a little work was brought up to excellent condition.