Satin, taffeta and velvet, however, were used. The corset of the Pfalzgrafin Maria, which Janet Arnold examines in her book Patterns of Costume 1450-1560 had an interior lining of linen but was a silk satin on the outside. The pair of bodies of Maria of Toledo was made of silk velvet. Queen Elizabeth had dozens of pairs of bodies made of "taphata, sattin and vellet" (taffeta, satin and velvet), according to the wardrobe accounts of the Master of the Queen's Closet. Silk satin and velvet were the most commonly used fabrics for richer folk. So, why use silk for a corset?

It's an incredibly strong fabric
It's period
It breathes wonderfully
You can wear the corset as an outer garment, and show off the fabric

MODERN EQUIVALENTS

COTTON DUCK CANVAS
Unfortunately, pure linen is nowadays hard to come by and period silk satin sells for $30 a yard. For purely utilitarian use, with no thought for period authenticity or pretty looks, the best fabric is cotton canvas, specifially "duck" or "drill" fabric. It can be found in any fabric store, usually for $4-5 a yard. Undyed, unstriped duck or drill in a cream or white color is best, if such is available, as it is both more period looking and less likely to bleed onto other garments when it gets damp or sweaty. This fabric:
Is the strongest and most durable fabric you can find for a corset; it stands up to repeated washings, and corset boning has a hard time poking through it
It's stiff, and doesn't crinkle or scrunch; this helps keep a smooth corset line
It's cheap.
You can get it in any fabric store
FANCY FABRICS
For someone wishing a fancier corset, perhaps one which can be worn over a chemise and skirt as an outer garment, (it's not perfectly period, but it looks nice) the general practice is to use canvas drill or some other plain, strong, cotton-based fabric for the inside lining, and a fancier cloth for the outside layer. There's a wide variety of fabrics to choose from.

Modern fabrics made to resemble their more expensive, originally silk-based counterparts-- brocades, shot silk, taffeta, and satin to name the big four--are period-looking, beautiful possibilities for outer layers of corsets.

Upholstery fabrics and brocades These are usually quite strong and unlikely to rip, though they have more give and stretch to them than canvas does. However, depending on what it is made of--synthetic or natural fabrics, and what kind of dye is used--there may be problems with shrinking while washing, bleeding of dyes, and (this is a problem with synthetic fabrics) a lack of breatheability while wearing it. This might seem like a small consideration, but when you're wearing a corset at high noon under heavy clothes, it seems much more pressing. My tapestry corset, though it looks great, is a sweatbox compared to my cotton canvas one.
Prices range from @ $8 to $15 a yard, depending on the type of brocade you're buying. Check the fabric store remnant tables for scraps of upholstery fabric; a corset doesn't