pattypurple

If you have a sign shop nearby go in and ask for their scraps. The corrugated plastic, like campaign signs are made from, is very lightweight but strong. I got an armload of various sized scraps for $10 and have been using it for almost a year (and I make lots of purses/bags). I've tried foam core, but it bends. Plastic canvas isn't strong enough to suit me.
I use an old rotary cutter to cut the plastic. Make fabric sleeves to put it in and leave one end open so it can be taken out when the bag is washed.

Earleen

I used a fabric sleeve and DH cut a thin piece of luan panneling with rounded corners.

quiltin chris

Nancy's Notions has something called Shape & Create and also Bag E Bottoms---these items are specially made to keep the bottom of your bag from being droopy.

Chris

Mad Mimm

I use template plastic or use those thin cutting boards you can get from dollar store.

traveler53

I have used the heavy template plastic and also put it in a fabric sleeve.

gellybean402

I use coreboard which I purchase at Joann's, cut out the size I need, and then I sew together a pillow case to fit the coreboard in. I don't sew one end so the coreboard can be taken out and the pillow case washed the same time the purse is washed.

kacklebird

wuv2quilt,
My hubby cuts me out the acrylic bases too

BMP

2 layers of plastic canvas works for me !!

PurplePassion

Our Walmart sells a heavy Pellon , that I use.

Central Ohio Quilter

I have some old clipboards that I have cut to make the bottoms of bags. Nice and sturdy, and will not sag. I cut them with a jig saw and sand the corners a bit rounded.