My 1999 v70 , has 206+ k miles on it. I flushed the transmission about a year ago. I have a problem in that when I put it in reverse it barely moves. If the selector is in reverse and I do not give the engine any gas the car will slowly move backwards. If I apply gas the car will shudder and hesitate and not easily move in reverse.

Make sure we use the transmission dipstick spout with funnel to refill.

First, check the level of the ATF. This is a 4 speed auto? What type of ATF did you flush it with? Did you have a shop do the flush or did you do it yourself?

Florida is mostly flat, thank you for that. When you give it gas in reverse, does the engine not rev nicely?? Suggestion: one of the emergency brake shoes may have fallen off and is blocking rearward rotation. Try jacking one of the rear wheels up and rotate it by hand forward and backwards.

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My back feels better when I sit in a Volvo seat

I topped up the fluid , 4 spd , Dexteon III, I did the flush myslef.

When I give it gas teh engine revs normally but the car does not move normally. it shudders and barely responds. If I do not rev the engine it will slowly move in reverse. I recall that recently when I did try to reverse up an incline the car shuddered and struggled to move up the incline . I will check the rear wheel procedure.

If both rear wheels move freely, then the problem is the tranny. Keep the car in park when jacking, of course.
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My back feels better when I sit in a Volvo seat

I have read some posts about transmission solenoids , Is that a possibity and where are these located

Because it actually engages reverse, I would rule that out. When a solenoid fails, the function it performs fails and nothing happens. Like torque converter lock up or shift change.
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My back feels better when I sit in a Volvo seat