You need to talk to the baby's doctor and have the baby evaluated. There may be a physical problem why the baby can't swallow. The baby may some kind of tactile sensitivity issue.
I'm not sure what you mean by finger snacks. Try fork mashed banana or mashed sweet potato. These are two of the first foods recommended when people start solids with regular food and don't use baby food. Give the baby a sippy cup of water and let him drink between bites if he wants to.
There is info on starting solids at www.kelllymom.com
at 10:46 AM on Nov. 13, 2009