Of all the clothes a woman wears, a wedding dress is perhaps most closely woven to her heartstrings.

But once the big day is over, wedding dresses tend to get quartered in a wide variety of places. Most end up hung in the plastic bag they were purchased in, between Grandma's fur and Dad's old flight jacket. More romantically, some are laid to reset in an old attic trunk for a private, dreamy winter's day.

whichever way you are storing, or plan to store your wedding gown, there is one thing to remember: Its fate lies in your hands (and hangers). Your dress will last for your granddaughter if properly stored. Here is additional advice gleaned from the Museum of History and Technology's Division of Costumes:

Begin by determining the style of your dress, for that dictates the storage method. If you have a fairly sturdy, light- or medium-weight gown, perhaps of Mexican cotton or chiffon, a well-padded hanger will do. Pay close attention to shoulder shaping and stufff with tissue if it seems slack.

A lightweight plastic bag goes over the gown, with the bottom open to prevent mildew. Hang away from direct light, but pay attention to where you're hanging it. Any place in your home subject to fluctuating temperatures and humidity, like damp basements or uninsulated attics, should be avoided. Constant temperature change can wreak havoc on any fiber.

If your wedding gown is of the heavier lace/net/silk variety, with beading or other detail, flat storage in as large a container as possible is recommended. This prevents stretching and sagging of heavier materials.

Plan the arrangement of your gown with as few folds as possible. All folds should be rounded out with a stuffing of tissue, concentrating the folds toward the outside of the container. Shaping of the dress, particularly the bust and shoulders, can be supported by crumped tissue from within. The arranged dress should then be wrapped in a clean sheet or muslin before final placement. d

For a professional touch, the Costume Division recommends "Permalife" paper, obtainable from TALAS, 104 Fifth Ave., New York, N.Y. 10011. This lining material neutralizes any acid, effects from the container itself.

Now that your gown is safe, remember your headpiece and/or veil. Virtually the same rules apply. If you wore a short, light veil, it can be hung on its own well-padded, covered hanger. For delicate laces, mantillas and full-length veils, container storage is preferable. Allow enough room for the height of the headpiece, supporting it on tissue and covering the crown. Again, arrange for as few folds as possible, padding them into rounded, not flat, edges.

If you can't bear to wear or dye your wedding shoes, they can be stored for posterity in shoe trees and wrapped in plastic. If you danced all night and they're a big dingy, have them cleand first by a shoe-repair service.

Clothes can be heritage, and a wedding gown is the prime example. If all of this preparation seems too complicated, among stores offering storage service for your new heirloom (including veil) are:

Garfinkel's: "Heirlooming Serving," cleaned and hermetically sealed in corrugated box with veil. Bring to F Street Bridal Salon or any branch's Better Dress or Designer Depts. Takes 2-3 months. $65.

Woodward & Lothrop: Inspected, hand-cleaned, placed on chemically-treated paper. Sealed in plastic on support form and doubled boxed. Takes 1 month. $60.

Royal Formal and Bridal: Cleaned and stored in windowed box, airtight. Bring dress to any of six area locations. Takes 2-3 weeks. $55.