If its shaking side to side could be a tire out of balance or maybe a mechanical issue (wheel bearing, alignment, etc). Probably not a safety issue, but it can wear the tires out prematurely which can be expensive. Warped brake rotors are the most likely cause if the steering wheel only shakes when applying the brakes.
i had the same problem with my 93 GC limited which has a solid front axle. in that case if the vehicle has a solid front axle check the steering stabilizer shock. what you do is remove the shock if it easily compresses and you kinda here liquid bubbling then it is bad. in my case i replaced it and the shaking went away. if you have a lift kit make sure to get a heavy duty shock. one more thing to check is the front brake rotors for any warpage. if the vehicle shakes after hitting a bump in the road its a good chance its the stabalizing shock.
bad rotors
Tires and/or wheels out of balance?
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I would start with wheel balance but the front end steering and suspension needs to be checked also.
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have your front brakes checked
What make the steering wheel shake is the tires that need wheel balance.
Your brake rotors are warped and need replaced/resurfaced.
Could be that the rotors are "out of round" and need either to be resurfaced or replaced
worn front end parts (steering or suspension) could cause a car to shake when appling the brakes.
Worn bushes or warped brake rotor. Replace faulty item.
Most probably
If the rotors are warped it can cause a shake when you hit the brakes.
Pulsation in brake pedal when stopping? yes and also a shake or shimmy in the steering wheel when brake. your brakes may also chatter
Perhaps front rotors are "out of round" and need to be either re-surfaced or replaced
Tires,inner tie rod bushings, if the steering wheel shakes when brakes are applied - brake rotors warped.
If the steering wheel shakes, but to car doesn't, when applying brakes - your front rotors are warped (if you have disc brakes)...if you have drum brakes, the drum could be cracked or the pads worn unevenly If the whole car shakes, and the steering wheel only seems to react to that, when applying brakes - see above statement, but apply to the rear end. If the whole car shakes, including the steering wheel - all four corners are bad, and you're an accident looking for a place to happen soon. In any case, go to your nearest service center ASAP.