Just got a used Craftsman riding mower with a 16HP Briggs& Stratton OHV engine, model #310707. Originally it would not start, click or do anything at all. I did a lot of cleaning on all the switches, charged up the battery and it cranked with an initial loud backfire. Started it again and it ran fairly good but had an occasional backfire. Did a basic tune-up, i.e.. New plug, air filter, oil change, valve adjustment (set at .004) and took off the electronic gas valve solonoid and draineed gas out of carb. Gas looked clean, no junk or water in it. Gas in the tank is new. Engine starts right up , but still runs with the occasional backfire at full throttle. It does have a range of running speeds and at idle it seems to run fine but I can see the governor is still surging a little. Also when you go directly from full throttle to slow idle, it always gives a louder backfire. The fuel mixture adjustment does not have much if any effect and it has a limiter on it. Any suggestions on what to do next to get rid of the backfire?

Hi,
Thought about your question a bit; I do not always "jump" in with an answer. I would be suspicious of the flywheel key first. Current ignition technology with the advance systems that help the engines pass the EPA certifications can allow an engine to crank and perform reasonably well with a sheared key.
If this is a manifest problem that has occurred where it was not before, that would the best guess. If it is something that has always been there, it is probably a cheap muffler. That happens, too. The "bean counters" work in 100ths of a penny on these things.
Peace,
Clarke

Clarke.
Thanks for the suggestions. I will look into this further this evening. The muffler is very loud ,like it is burned out.

I also agree it seems like the muffler needs to be replaced and if the backfireing contunius try replacing the piston rings because the addition of oil to the great amound of gass being put into the cylender may cause a large backfire... please excuse my spelling I have a slight problem with it