replaced tire, now wheel flexes side to side I have an 85 Raleigh that until yesterday had never had its rear tire replaced over the life of the bicycle. Before I replaced it, the wheel seemed fairly stiff. I don't know if the old tire was so dried out it ed lending support or what.

I'm wondering if I need to get something adjusted or if a bit if flex is ok. Is this normal?

Edit: by flex, I mean I tightened down the bolts, so the axle is tightly locked to the frame. However, when I first took the bike off the rack, the tire stayed in the same place on the ground, but if I shook the seat side to side, it would hit a frequency where the axle would move side to side, but the rim would sort of flex backwards and forwards.

Also, by stiff I meant it didn't do this before, not that the brakes were rubbing or anything.

Edit 2: There were questions about how well maintained this bike was, the previous owner said it was used as an indoor exercise bike, and when I bought it it it was on the bike exercise stand. It didn't have a front wheel, and based on the wear on the rear tire, I don't think it was used much, so as far as I can tell, it just sat in someone's basement for 30 or so years.
There should be no flex.

It's possible you haven't reinstalled the wheel correctly; and the axle is sliding around in the dropouts. If that's not the case, I assume you're talking about lateral wobble when you hold the bike frame still and wiggle the wheel rim. That indicates hub bearings in dire need of replacement.

You say the wheel felt stiff before replacing the tyre; the chances are the tyre/rim was rubbing against the brake pads. In changing the tyre you most likely knocked things about a bit and nudged the brakes so that they no longer rub on the tyre/rim, exposing the play in the hub bearings that was already present.

Much less likely: If you're talking about a different kind of flex (i.e. the wheel rim is actually deforming under moderate force), you've probably cracked the rim while replacing the tyre.

It sounds like a trip to your LBS to me. Wheels should not flex in any of the ways described above, and a bike which hasn't had a tyre change in 29 years will almost certainly have been neglected in other ways too. You don't seem to have a great deal of experience, and most likely won't be able to spot potentially dangerous problems. Take it in and ask for a full service.