Looks as if I'll be needing to change the mounts in the V70 (what next?)

Which mounts are the usual suspects? The engine often shakes when shutting off, and when starting. The upper mount looks to be in good condition, but you can never tell. Any brand better than another?
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Obama, One and Done!

two mounts are suspect, upper mount to the firewall and the lower front by the crank pulley.

The lower mount is fairly easy. Jack stands are needed as the engine gets lifted 1/2 inch to take load off of mount while the right front wheel is off. Use OEM only for replacement.

Upper mount needs to be visually inspected for cracks. Normal life is 90-100K miles. It is a pressed fitting, so many of use go the poly route to keep it easy to replace. Some swear that there is more engine vibration in the steering wheel from the poly, I never noticed a difference.
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My name is Klaus and I am a V♂lv♂holic

I think that I'm going for broke and change the upper, lower and transmission mount. I'm not a fan of fishing for a fix, and ending up under this POS several times for the problem. I'm going with OEM parts from the Volvo Dealership. Replaced the mounts on my old 245 with a set from Meyle, and they never did stop buzzing. Oh well. Wonder what next?
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Obama, One and Done!

How many miles on your car? Klaus is right, the upper mount is the only one that typically goes at <150k. My money is on that one.

Did you take a really good look at the rubber on the upper mount for cracks? The rubber on my 850's upper mount was dried out and cracked which allowed the engine to shake more than it should. Sounds similar to the symptoms you described. I put in the IPD poly and had no problems with it. If you replace any of the other mounts definitely use OEM. The IPD upper mount is an easier install because the factory mount is pressed in. No need to get under the car if this is the only mount you need...:)

I have never heard of the tranny mount going and lower front engine mount usually lasts a long time. Mine is still going at 200k. Here is a description of how to troubleshoot and replace the lower front mount (passenger side) from Volvospeed. It is for 850's and S/V70's through 2000, but I'm guessing your 2001 has the same mount.

http://volvospeed.com/volvo_repairs_how_tos/engine_repairs/front_engine_mount.html

Car has 130K on it. I can't see any cracks in the upper mount, but when starting or cutting the engine off, you can feel a jolt from the engine.
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Obama, One and Done!

Does it move too much or shake a lot at idle?

You might also want to check your vacuum lines. Also, a while ago a friend of mine's 740 shook pretty badly and it turned out to be the fuel pressure regulator.

No, when running it is as smooth as silk. Just lunges on start up and shut down. You can feel it when you shift out of park or between reverse and drive.
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Obama, One and Done!

No, when running it is as smooth as silk. Just lunges on start up and shut down.
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Obama, One and Done!

On our 2005 S80 2.5T, the upper mount was the first, and so far only, one to fail at around 110,000 miles and 7 years old. My local Volvo independent mechanic tells me the the upper one is generally the first to go. I think I paid about $55 for a Volvo blue box replacement. Remembering back to the time I replaced our 740 motor mounts with non-Volvo parts and the the disappointment that followed, I've decided motor mounts are one of those things where I would rather not "stray from the village".

How about the rubber isolators at the ends of the upper torque bar, where it mounts to the chassis - are they still in good shape. I don't know if they typically wear out or not.