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The native cartridge for the K31 is 7.62x55mm. The .308 is 7.62x51mm. Did you mean simply that you can use .308 caliber bullets, or are there some K31 rifles which are chambered in .308? I don't know much about them, which is why I ask.

".308" as in .308 diameter for reloading, apparently i ommited a proper reloading reference. I reload for everything so i typically think in those terms first before considering purchased ammo. yes, for reloading you can use the plethora of .308 bullets available for a swiss. Indeed the swiss cartridge is "7.5x55"

Yes, not to be mistaken, the 7.5x55 swiss K31 or k11 do NOT take 308WIN cartridges.
... however the K31 reload data is also very similar to 308WIN since the case capacities are very similar (with x55 being slightly larger) as is the pressure rating (NOT the k11 though)

I have two 24/47s, two k31's, 1 no4 mark1, and of course a few mosins.
Get a k31, hands down. if you reload then even better as it is a .308.
absolutely superb rife and great trigger. I think they are all tack drivers.

if a k31 isnt an option then i would probably suggest the 24/47 mauser as a shooter as nearly all of them still have excellent bores and shoot well.