The BFW M 31 was designed in 1932 by Willy Messerschmitt to be an inexpensive and robust trainer and sportplane in the same vein as the M 17, M 23, and M 27. It was developed to use readily available German produced engines and the sole M 31 (W.Nr 607) was initially fitted with the five-cylinder BMW Xa radial engine, although the more powerful four-cylinder Hirth HM 60 was ultimately installed.
The wings and horizontal stabilizer were of wooden construction and ply covered, while the fuselage was of metal tube construction with fabric covering; the control surfaces and rudder were wooden with fabric covering.
The propellor was laminated wood of two types.
An unusual feature of this little trainer was the joystick in the forward cockpit, which could be rendered inoperable by simply turning its grip. Other notable features included a freely swivelling tailskid, a small luggage compartment aft of the rear cockpit and large low pressure tires for softer landings, especially when used in its trainer role.
Despite being exhibited at the 1932 Deutsche Luftsport Asstellung (German Sport Aviation Exhibition) or DELA, the M 31 generated little interest and the project was abandoned. The M 31 was registered D-2623 in 1933 after being fitted with the Hirth engine and in 1934 was acquired by the RLM where it most likely was used in its intended role as a trainer.

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