Upgraded scope on rifle and now I can't shoot groups - Help!

Check and do all of the basics.
Make sure mount and rings are torqued properly.
Scope is level.
Eye relief is set to work with your normal shooting position, do this on max power with no shadow around sight picture. (Max power is shortest amount of eye relief)
Focus the reticle properly.
Adjust parallax for the range you are shooting, not just by the numbers, but by slightly moving you head side to side or up / down and make sure the reticle stays in place on the target.
Read articles on these settings and procedures if you do not fully understand them, they are more important than you may think.
 
What rifle action did you put it on ? Does it make any difference if the rings are front or back rings , as they can cause pressure problems at times ? I have seen this with Browning actions where the rings look nearly the same but don't interchange front to back and work out well . Is the new scope touching the barrel ? Are the rifles action screws still tight ? What type of stock is the rifle mounted in , wood , synthetic , laminated ? What type of shooting platform are you using , bags , ect. ? Is the barrel still clean any carbon ring or other build up in it ? So many variables so many questions that need answers to figure it out .
I too have seen that on Ruger rings.
 
I once had a similar problem. Gun would not group with new scope. I wasted more ammo than I should have, but when working with the scope and rings, it was like the scope just suddenly settled in the rings and all was well, and 30 odd years later, it is still shooting true. Back then I probably was using Weaver rings.
This was a Remington 788 in 22-250. Still shoots too good to be true.
 
Possibly already said and late response, but, you mentioned that you are using different rings so the bell clears the barrel. Okay so now the centerline of scope is further from center line of barrel. Did you change the cheek rest to match? If not I would. Your spot well has changed due to the height of the scope change. Need to balance it all back out. Incorrect spot well and height will cause double grouping and wondering shots.
 
All of the above are very good pointers and advice to your problem. It's up to you now to figure it out. Your not the first one that has ever had this issue and you won't be the last. All I can say is figure it out, learn from it.........if that doesn't work then best I can tell you is sell the scope and run down to a local "Gibson's" and pick up a good ole Tasco scope.

Sorry I had to.
 
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