System component failure can cause the airbag warning light to illuminate. Stored fault codes should be diagnosed to help isolate the cause of the problem. A recall for the driver's side airbag applies to 1994 & 1995 models only.Google+
Car Problem Reports
Hyundai Elantra Recall for Defective Airbag System that Causes the Airbag Light to Illuminate
Hyundai Elantra Problem
Average Mileage: 132,500 mi (120,000 mi - 145,000 mi)
Visitor, 1998 Hyundai Elantra, 120,000 mi
I also had the airbag light on for quite some time. took my 98 elantra in to dealer for other repairs and they fixed the airbag issue no question asked by me. They did't even mention it too me. They just took care of the problem with the air bag system. I read there was an issue with a air bag control module in the ceneter console/shifter area known to go bad. Car was way out of warranty. Now, if I can just get CEL code P0442(evap system small leak detected) fixed I can pass inspection again.
Visitor, 1996 Hyundai Elantra, 145,000 mi
It is still illuminated. The car is so old we haven't wanted to pay money to fix the problem.