SF: is rated for 1988 and later engines.

SG: is rated for 1993 and later engines.

SH: is rated for 1996 and later engines.

SJ: is rated for 2001 and later engines.

The Current Rating now is "SL" and it work with all automotive engines currently in service.

API intentionally omitted "SI" rating because it was commonly being confused with "Other" oil ratings.

If your manual says it will run on SF, SG, SH, SJ, :

Then it will run with SI, but I'd buy some fresh oil.
As "SL" was introduced in 2001 so your "SI" oil is pretty old.

Short answer is YES you can use "SI" but any marked with "SI" is pretty old oil.

Here is a link that might be useful: API Oil Ratings

Go to Advance Auto Parts or Autozone or a similar auto parts store and buy some of their house brand SAE30 oil in a quart bottle -- it will be cheaper than a smaller bottle of SAE30 oil at Home Depot.

'I don't want to buy the expensive B&S warranty certified oils or do I'

Ummm...20 ounces of oil once a year? Two quarts of the most expensive oil you can buy (Royal Purple 'Max-Cycle' 10W30 motorcycle oil for air-cooled service) is $24. That's 64 ounces, which will change your oil three times plus a little extra. That's $8 a year for the best you can get. Okay, how about my personal favorite for the Tecumseh or Briggs engine that specifies SAE30HD down to 32 degrees - Opti-4 SAE 30HD (non-synthetic) in 20 oz. bottles (no measuring) for about $35 for a six-pack - that's six years' worth if you change once a year, about $6 a year. Moving on down the line, my next choice would be Quaker State SAE30HD or Castrol SAE30HD. So, there is really no justification for the notion that ANY oil is 'too expensive' for a mower at a maximum of $8 a year. I use the Royal Purple in my LB 22271 with Honda commercial GSV190/OHC (iron bore liner) and the Opti-4 in my LB 10684 with Tecumseh LEV195 (aluminum bore). After break-in with Quaker State, the oil was a little gray with aluminum particles. After using the Opti-4 for two years, the current oil having been in over a year, it's still so transparent that I can hardly see it on the stick. Opti-4 has a greater parts-smoothing action (eutectic action) than most oils, and it really works in these aluminum bores.
Okay, I'm tired of writing, so I'll quit. Just think about this before 'saving money' on mower oil - maybe it would be better to get indefinite life out of the engine.

You're right, I wasn't thinking when I referred to cost of oil. Can't say I even knew what B&S would charge. I'm just tired of so many companies crying wolf and that I would ruin my car, lawnmower, printer, etc, if I don't use exactly what they market so my hackles rose when I read their warning in the manual. Really now, how many of these products are truely unique to the device? Agree?

All other things being equal (which they're really not), there is a difference between 'air-cooled' service and conventional automobile oil. If the B&S oil is so rated, it sure wouldn't hurt to use it, and it is convenient in the 20 oz bottle. And as we already know, it isn't a matter of economy.

Having the Best Oil is the Most Critical Decision for the Life of Your Engine. In the 70's Sae.30 was typical. I now use Amsoil Air Cooled Multi Grade in my B&S Quantum . Royal Purple was used extensively in my Open Wheeled Modifed until my Hip Replacement. Probably should of drank a ounce a day of either and put off the Hip Replacement lol . As Saxman has so concisely indicated don't be cheap on Engine Oils .

I wonder if the SI oil isn't really SJ or SL with the second letter poorly printed. I would be very surprised if HD was selling oil so old that it did not appear on the API charts.

For what ever it is worth I use synthetic oil with the weight recommended by the owners manual. I've found that the synthetic oils don't darken and carbon up like non-synthetic engine oil. In an engine with a 20 oz. sump and no oil filter that's important. It costs about 2/3 of $5.00 per year for an oil change.

Please please enough abought oil. Buttom Line any name brand 10w30 is perfect. Just change it every 40 hours of use or once a season and your engine will outlast your deck. Happy grass cutting