Stiff tweed waistcoat

[Lady Grey]

If it's a good quality tweed, linings & construction, I suggest a "gentle" Jocking, if you can't wait to wear it in.
A gentle rinse in water, a gentle pat and roll in a towel, a gentle pat into shape, a gentle dry on a towel, a gentle iron/steam with an ironing cloth.

Actually, thinking as I write a steam press with an ironing cloth protecting the fabric may also do the job and help soften it.

[Todd Bradshaw]

Tweed itself, even something like overcoat weight Harris Tweed, isn't very stiff. What makes for a stiff waistcoat is the interfacing, which may be sewn-in, or more often is fusible and bonded to the back side of the tweed. A lot of waistcoats have the entire front interfaced in order to give them some shape and crispness. Rather than doing anything drastic, I think I'd try just wearing it for a while, as it will probably soften up somewhat. I suppose you could also work the cloth, bending and flexing it in your hands, which will soften most stiff leathers and fabrics to some extent without harming them. Most modern interfacings are non-woven, their fibers bonded together, and working them will tend to stretch and relax the bonds between them somewhat. Since steaming is how you remove fusible interfacing from wool fabric, I'd be pretty careful trying to steam it into submission. If it is fusible, you really don't want to delaminate it from the tweed.

[Richrail]

So what I've done so far is to run it through the dryer with NO heat and three new tennis balls it seems to be working. And later the dogs get new toys