You've gotten a lot of conflicting advice. Let me add mine.

Without going through the numbers in detail, Paul, OH3LWR's analysis
looks sound. However, he neglected one factor. The skin depth is also
inversely proportional to the square root of the permeability. Some
stainless steels are ferromagnetic, with a permeability I'd guess at 100
or more. That reduces the skin depth, and therefore increases the RF
resistance, by at least a factor of 10. If you do the analysis with
realistic numbers, you'll find that loss can become at least several dB
if the wire is magnetic, and worse with longer (40 or 80 meter) dipole
lengths.

So my recommendation is to check the wire with a magnet. If it's
magnetic, expect longer antennas to be quiet and broadband (which
amateurs crave) but lossy (which most don't seem to care about).
Non-magnetic stainless isn't likely to produce objectionable loss,
except perhaps at an 80 meter dipole length or longer.

You can get a qualitative feel for the loss by comparing the 2:1 SWR
bandwidth of an antenna made from the wire with the bandwidth from a
dipole made from copper wire. The broader it is, the lossier it is.

Roy Lewallen, W7EL

Dave wrote:
I recently acquired a large quantity of very flexible stranded
stainless steel wire at a garage sale. It is about 0.85 mm (around
1/32 inch) in diameter and extremely strong. I was wondering if this
could be used for wire antennas for HF. I seem to remember seeing
something about SS not being ideal. Is this a real consideration or
just a matter of being too finiky?

Thanks - Dave