Tauranac designed the BT34 in 1971 following Jack Brabham's sale of his share of the team. The car's most striking feature was its twin radiators positioned forward of the front wheels on either side of the nose, giving the front of the car an unmistakable claw-like silhouette. Only a single BT34 chassis was constructed. Graham Hill was assigned the new car while Tim Schenken drove the older BT33.
The BT34 made its race debut at the 1971 Spanish Grand Prix, where Hill retired with steering problems. A troubled campaign followed: Hill crashed at Monaco, finished tenth in Holland, retired in France with a broken oil pipe, was involved in a race-start incident at the British Grand Prix when a botched flag drop caused a collision with Jackie Oliver's McLaren, finished ninth in Germany, achieved a creditable fifth place at Austria, and retired in Italy with a broken gearbox. The season ended with a crash in Canada and a seventh place in the United States.
Because only the best-placed car from each constructor scored points toward the Constructors' Championship, Hill's fifth at Austria did not count — Schenken had already scored points with the BT33 in that race. Brabham finished ninth in the Constructors' Championship with five points, all attributed to Schenken's efforts in the BT33.
At the season's end, Ron Tauranac decided the financial risk of Formula One was too great to bear alone and sold Brabham to Bernie Ecclestone for £100,000. Tauranac initially remained as designer and factory manager, but left in early 1972 after Ecclestone reorganised the team without consulting him.
For 1972, Ecclestone retained Hill and signed Carlos Reutemann as his new lead driver, placing the Argentine in the BT34. Reutemann announced himself spectacularly at the season-opening Argentine Grand Prix by taking pole position on his Formula One debut, though he finished only seventh in the race. He retired from South Africa with fuel system failure and later broke his ankle in a Formula Two accident at Thruxton, which interrupted his season.
With Reutemann sidelined, Brabham enlisted Brazilian Wilson Fittipaldi to drive the BT34 at several races. Fittipaldi's results were modest — an eighth in France, twelfth in Britain despite stopping with broken suspension, and seventh in Germany — before he retired from the final four races with a succession of mechanical failures.
The team scored seven World Championship points in 1972, four by Hill and three by Reutemann, finishing ninth in the Constructors' Championship for the second consecutive year. The BT34 was replaced by the Brabham BT37 for 1973.
The BT34's lobster-claw front radiator arrangement was an inventive but ultimately unsuccessful attempt to improve aerodynamic efficiency by relocating the heat exchangers away from the conventional nose position. The concept was not adopted by other teams and Brabham itself reverted to more conventional packaging with subsequent designs. The car represents the final chapter of Ron Tauranac's tenure as Brabham's chief designer, closing an era that had begun with Jack Brabham himself.