More than likely if you are approved for SSD benefits your children will also receive a benefit based on your earnings record.  In order for this to happen, your earnings over the years must have been sufficient to the point that there is money left on the record for your children.  It has been my experience that most people who qualify for SSD have money left over so their kids also receive some benefit.  As with SSD for yourself, the amount that the children receive is based on your earnings when you were working.

Just because you have applied for SSD benefits does not mean that the Social Security Administration will automatically process your kids claims.  If you are approved for SSD benefits you must also make the administration aware that you have minor children (once kids turn 18 their benefits stop).  You will likely have to take birth certificates in to your local social security office and they can then process those benefits.

If you only qualify for SSI benefits, then your children are not entitled to any benefit, based on your disability.   This is because SSI is a need based program and as a result there are no benefits available to children of a disabled individual.  However, if the child is disabled, then they very well could qualify for SSI benefits as a result of their own disability.