Your child can get benefits if he or she is your biological child, adopted child or dependent stepchild. (In some cases, your child also could be eligible for benefits on his or her grandparents’ earnings.)
To get benefits, a child must have:
A parent(s) who is disabled or retired and entitled to Social Security benefits; or
A parent who died after having worked long enough in a job where he or she paid Social Security taxes.
The child also must be:
Unmarried;
Younger than 18;
18-19 years old and a full-time student (no higher than grade 12); or 18 or older and disabled. (The disability must have started before age 22.)
The child may qualify under the parent's disability.
From http://www.ssa.gov/pubs/10085.html :
Who can get child's benefits
Your child can get benefits if he or she is your biological child, adopted child or dependent stepchild. (In some cases, your child also could be eligible for benefits on his or her grandparents’ earnings.)
To get benefits, a child must have:
The child also must be:
The child may qualify under the parent's disability.