Check these locations:
Below the barrel stamped into the crankcase. On the front of the engine stamped either side of the crankcase join. Below the clutch / transmission area. Rear of cases below carburettor area.
By far the most common location is on the steering head. It may also be found on one of the rear downtubes or on the front downtubes.
Other locations include: top tube below fuel tank; lower frame rails; swing-arm pivot area.
Motobecane Mobylette 1968: Forward of the rear wheel axle on left side.
Matchless pre-1958: Directly below saddle on upper frame rail joint.
Matchless 1958-59: rear of front downtube.
Matchless 1960-67: right downtube below headstock.
Rigid frames: usually stamped on the lug beneath the saddle on LHS
Plunger frames: saddle lug (same as rigid), or on the steering head, LHS
Swing arm frames: stamped into steering head and/or into a steel ID plate pop-rivetted onto the steering head.
AMC AJS/Matchless from c1935
Engine numbers usually start with the year of production, followed by model designation, and completed with the production number of the motorcycle.
(Source - Wikipedia)
Ariel Serial Numbers
BSA Serial Numbers
BSA Numbering System
BSA Frame Numbers at NSW BSA Club
BSA Frame Numbers
BSA at sunnymeadcycles (PDF)
BSA Numbers at moto-anglaises.com
BSA C15 Serial Numbers
DKW Vehicle Identification
DKW NZ350 Serial Numbers
Frame & Engine Numbers
NSU Max - (1)
Also Automoto, Grifon and Meteore
See also under Penton
Sachs 98ccm Modell 1932
Velocette LE Engine & Frame Numbers
Velosolex engine serial numbers
This page includes information on Vespas made under licence by Douglas, ACMA in France, and Motovespa in Spain, along with those marketed in the United States by Sears under the Allstate marque.