Originally rayon was a "dry clean only" fiber. However, the fiber producers discovered that they could create washability in rayon by putting certain finishes on the surface of the fabric after it was knitted or woven. So, today there are both washable and "dry clean only" rayons available in the market.
Anytime a rayon garment, labeled "dry clean only," is washed, it can shrink tremendously, sometimes as much as “two or three sizes”. Other things may also happen, the garment may fade, or a printed pattern may bleed. The fabric may lose its soft hand, the rayon that was once soft and drapeable may become stiff and harsh.
On the other hand, most of the washable rayon garments today are labeled "hand wash, cool water, drip dry or dry flat." And, it's important that these directions are followed, because when rayon is wet, it actually loses 30% to 50% of its strength. So, hand washing, like the label says, is the best.
Tip! Learn some care instructions for rayon at Housekeeping Here.