You need to get elastic from a doll supplier.  I used regular "round"
elastic when I fixed my daughter's Samantha.  It is looser then it
should be, but is holding for now.  I've since purchased the proper
elastic and will do the changes when the current elastic breaks again.

The supplies I used are:

round elastic
needle nose pliers
small brass eyelets

You'll need to take the head off of the doll and unstuff her.

Then cut the elastic in each leg.

After this is one look "into" the leg, you'll see a cupshaped thing. Use
the plier to take it out of the leg, carefully.

Discard old elastic.

insert new elastic into cupthing so that the rounded part faces you. 
Use a brass eyelet to secure elastic.  (I used two.)  Push down the 
brass eyelet and then tie a knot in the elastic to keep it in place.  
Replace the cupthing in the leg. 

Thread the elastic into the body and thru the second cupthing.  Pull
tight and put on another set of brass eyelets.  

Repeat on second leg, restuff and replace head.

This should work.  I hope I've explained it well.  Part of it will
become clear once you get inside the doll.

    Source: geocities.com/mom4max