Welcome aboard.
Model numbers were not assigned until the late 1950's and your gun was made well before that. The barrel was obviously shortened and a front sight re-attached.
Stephen, does it have markings like this? Notice the "V" prefix. That would mean it was originaly an Aussie WWII Victory Model (a War time Lend Lease M&P).
It's been chopped and channeled for sure, in my view that gives the old warhorse character and maybe a new lease on life...The two Smiths in my current EDC rotation both fit that description...
The OP said it's "38 S&W" which means the .38-200 caliber is correct...Welcome to our forum, and please post some more pics from all angles......Ben