Replace rear bushing in 2001 Malibu

Carefully,clamp off just one rear at a time and then try one front at a time,it should be just one of the wheels causing the shake.Once you get down to the one or two causing the problem don't forget to check hub runout,wheel runout and wheel balance too.Sounds like rear to me.

Sound like out of balance tire or a separated tire or bearing but, the two most common causes are the ones. I suggest visit some tire shop and would like to have the tires inspected and balanced.

Some customers may comment on shaking/vibration in the steering wheel, floor or seat while driving at highway speeds (typically between 60-72 mph (96-115 km/h)) on smooth roads.

These specific vehicles may be sensitive to various rotating mass assemblies, especially if they are considered to be out-of-balance.

In order to correct this:
1. Visually inspect the tires and the wheels. Inspect for evidence of the following conditions and correct as necessary.
- Missing balance weights
- Bent rim flange
- Irregular tire wear
- Incomplete bead seating
- Tire irregularities
- Mud/ice build-up in wheel
- Stones in the tire tread

2. Set the tire pressure to 30 psi (205 kpa) COLD.

3. If the road test indicates a shake/vibration still exists, check the imbalance of each tire/wheel assembly on a known, calibrated, off-car dynamic balancer. If any assembly calls for more than 1/4 ounce on either rim flange, remove all balance weights and rebalance to as close to zero as possible.

Important: Some GM dealers may have a Hunter GSP9700 Road Force Balancer. This will simplify Step 5 by not requiring dial indicators. If a Hunter GSP9700 machine is available, it may also be used to measure the radial force of the tire/wheel assembly. A guideline here is 18 lbs or less.

4. While on the balancer, measure wheel runout. If radial or lateral runout exceeds .020 in (0.50 mm) for aluminum wheels (.030 in (0.76 mm) for steel wheels), replace the wheel.

5. After confirming wheel balance and wheel runout, if any changes were made, road test the vehicle again.

6. If the smooth road shake/vibration still exists:
Important: The completed worksheet must be attached to the hard copy of the repair order.

Record Radial Force Variation readings if you have access to Hunter GSP9700 Wheel Balance equipment. Use the worksheet shown in this bulletin to record the readings.

If one or more of the tires have RFV readings in excess of 18 lbs, match mount the tires to get below 18 lbs. Readings of 12 lbs. or less are preferable for critical customer concerns.

If the RFV can not be reduced to an acceptable level, replace the affected tire with one obtained locally.

The screened tire program is no longer in effect for Bridgestone/Firestone, Goodyear and Michelin. Low speed screened tires are available from Continental General only, and only for the Buick LeSabre.

Road test the vehicle to ensure the shake/vibration has been resolved.

7. Replace both lower control arms on vehicles built prior to the VIN breakpoints shown. The new lower control arms may provide an incremental improvement to the vehicle ride. Customers who have become "tuned in" to the shake condition may still feel some shake in the vehicle after the new lower control arms are installed.
Refer to Lower Control Arm Replacement, (refer to the Parts Information table below for SI document ID numbers).

Important: THE CONTROL ARMS SHOULD ONLY BE INSTALLED ON VEHICLES IF, AFTER THE TIRE AND WHEEL DIAGNOSIS AND REPAIRS HAVE BEEN PERFORMED, THE VIBRATION CONDITION STILL EXISTS.

Hope this helps; also keep in mind that your feedback is important and I'll appreciate your time and consideration if you leave some testimonial comment about this answer.

Thank you for using Fixya, and have a nice weekend.

If it only does it during braking, it's not an axle. Likely culprits are warped rotors or bad suspension bushings.

A warpped rotor will cause the brakes on that rotor to grab and release as the rotor goes around, causing a shake. This is often felt in the brake pedal as a pulsing as well.

Failed front suspesion bushings can cause this as well, esppecially on front wheel drive cars.. When you are accelerating, your wheels are pulling the control arms forward, but when you brake, the control arms are pushed backwards. So, depending on what bushings are worn out, your alignment can change pretty drastically going from accelerating to braking or vice-versa. This would also account for the moving/hitting sensation you described. To check this you need to jack up the front of the vehicle and check the control arm bushings, as well as any other bushings for links/parts connected to the control arm.

Computer testing is not going to find most mechanical failures. The computer systems in your vehicle controll electrical circuits.
It sounds to me like you may have some suspension bushings that are worn out. If it feels like the front (i.e. the sterring wheel is shaking, then check all the front suspension parts for looseness and wear. If it feels like the rear, make sure that the strut arms for the rear suspension do not have worn out bushings. Check all of the struts and/or shocks.
I had one of these one time that would be cruising down the highway with no problems, then you hit a rough spot in the pavement or a small pothole and the thing would start shaking so violently that it was threatening to go off the road. It turned out to be worn out bushings in the rear suspension.

I had this problem also. I had the rims cleaned, balanced the wheels and replaced the shocks. Each action helped a bit but replacing the shocks was the most improvement.

did you retourque your wheels?

tie rod more than likely attached to the rack and pinion

Check for a damaged wheel rim- the wheel balancer should have detected this, but may have missed it.
Check for defective tyre- new tyres can have faults -rotate wheel while jacked off ground, look for bulges, lumps or tyre runout when rotated.
Check for looseness of tie rods and steering box etc.
Check wheel bearings are ok.

Check for runout in your wheel bearing hubs. You can also hit your e brake lightly and see if it shakes then. If it does, it is in the rear rotors which will also warp.