Those of us with 96-00 Elantras commonly referred to as the J2 (should be RD, but that's another topic) all know the frustration of trying to find parts to modify our cars with. Here's some easy rules of thumb to go by:
Engine/Intake
If it fits a 97-01 Tiburon, it will fit your 96-00 Elantra. The engine, clutch/flywheel and virtually all of the transmission are the same between these cars.
Above is a lightweight flywheel that again bolts right on.
A lightweight crank pulley for the RD Tiburon that can bolt right up to the crankshaft.
Headers/Exhaust
Headers will bolt right up. Headers for the 01-06 Elantra and Tiburon will need the downpipe to be shortened. Catback exhausts designed for the Tiburon will generally fit, but often will need some extra hangers to work with the Elantra. Your exhaust shop should be able to fabricate these.
Suspension/Wheels/Brakes
If it fits a 97-01 Tiburon, it will fit your 96-00 Elantra. The suspension is again identical, and parts made for the Tiburon will bolt right up. Springs, struts, sway bars, strut bars, brake pads, rotors, drums, sway bar bushings, all will fit. Wheels are the same between the two cars also. For people considering a bigger rear swaybar, the best bet is to look online for one. The one from the 03 Tiburon will work with some bending in of the ends, about 1/2 inch on each side. Otherwise it will rub on the rear struts.
The Tiburon rear sway bar modified to fit. The long-term effects of bending the bar are not known.
Above are Tiburon lowering springs and KYB GR-2 struts.
Interior
The interiors of the two cars are completely different. You may be able to swap the front seats though.
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Generally speaking, the mechanicals are identical between the 96-00 Elantra and the 97-01 Tiburon. So if it fits the 97-01 Tiburon, it will fit your 96-00 Elantra.