The 507 frame is a shortened 503 frame, the wheelbase having been reduced from 2,835 millimetres (111.6 in) to 2,480 millimetres (98 in). Overall length is 4,835 millimetres (190.4 in), and overall height is 1,257 millimetres (49.5 in). Curb weight is about 1,330 kilograms (2,930 lb). The body was almost entirely hand-formed of aluminium, and no two models were exactly the same.
Front suspension is parallel double wishbones, with torsion bar springs and an anti-roll bar. Rear suspension has a live axle, also sprung by torsion bars, and located by a Panhard rod and a central, transverse A-arm to control acceleration and braking forces. Brakes are Alfin drum brakes of 284.5 mm (11.2 in) diameter, and power brakes were optional. Late-model 507s had front Girling disc brakes.
The engine is BMW’s aluminium alloy OHV V8, of 3,168 cubic centimetres (193.3 cu in) displacement, with pushrod-operated overhead valves. It had two Zenith 32NDIX two-barrel carburetors, a chain-driven oil pump, high-lift cams, a different spark advance curve, polished combustion chamber surfaces, and a compression ratio of 7.8:1, yielding 150 metric horsepower (110 kW) DIN at 5,000 rpm. It is mated to a close ratio four-speed manual transmission. A contemporary road test of a 507 with the standard 3.70:1 final drive was reported in Motor Revue, stating a 0–100 km/h (0-62 mph) acceleration time of 11.1 seconds and a top speed of 122 mph.