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Having a hard time keep the rifle from moving

Benchrest shooting. When I get ready to take the shot the crosshairs keep moving around on the target. The front rest is a Shadetree with 3 inch bag and the rear bag is a Protector. I am thinking I need a different rear bag, maybe ? The rifle is a Savage model 12 in 223 with a 30 inch full bull barrel on an HS precision stock..
 
Can you share a picture of your setup? You said you’re shooting a 3” bag and HS stock. Do you have a bag rider on the forend of the stock so it rides the bag properly?

Do you have any shoulder contact with the stock as you go to fire? I shoot free recoil with my 6 PPC. Just a light touch can move the crosshairs.

Is your trigger pull weight causing the movement as you squeeze the trigger?

Is your trigger finger square on the trigger as you squeeze the trigger or are you slightly pushing from the side?
 
In addition to the above responses I’ll ask if the bench top is concrete and stable or plywood and perhaps flexing slightly when you lean forward ?
Added thought, a 30 inch bull barrel may be taking the rifles balance point to far forward making the rear too sensitive.
Jim
 
Benchrest shooting. When I get ready to take the shot the crosshairs keep moving around on the target. The front rest is a Shadetree with 3 inch bag and the rear bag is a Protector. I am thinking I need a different rear bag, maybe ? The rifle is a Savage model 12 in 223 with a 30 inch full bull barrel on an HS precision stock..
If you are using a 3" wide front rest bag, but the fore-end of the stock is not 3 inch with a flat bottom, that is part of the issue. They make front bags for narrower front stocks that should work better.
 
It is not parallax. The bench is brand new made of 2x6 and is solid. My finger is square on the trigger which is a Jard set at 8 oz.
How to tell if I have the right rear bag ?
 
Is your seat attached to the bench? I see so many of these and I am not a fan, at least for serious work.
I am with others on bags fitting front and rear, the reason I have so many I guess.
 
It is not parallax. The bench is brand new made of 2x6 and is solid. My finger is square on the trigger which is a Jard set at 8 oz.
How to tell if I have the right rear bag ?
The stock should fit between the ears snug. There is an argument of touching the stitching vs not touching. Regardless if you’re touching or not, it will not cause reticle movement prior to firing if it’s snug. The incorrect rear bag or bag fill can cause vertical on target.

Some rear bags get a bulge on the bottom that allows them to rock easily. Make sure your rear bag doesn’t have a bulge. If it does try getting or making a donut for the bag to sit on to see if that corrects the issue.

How tight are the front ears squeezing your stock? You might try tightening the ears down on the forend if they are not already tight.

There are a lot of factors that will contribute to your issue. If you have narrowed everything else down and you’re positive the issue is the rear bag, I would suggest trying a different one before purchasing if you know anybody that will loan you one.
 
It is not parallax. The bench is brand new made of 2x6 and is solid. My finger is square on the trigger which is a Jard set at 8 oz.
How to tell if I have the right rear bag ?
Parallax has nothing to with your bench, the material it’s made of nor your trigger.
It’s a phenomenon with scopes. What it does is quite similar to what you describe
 
If you are putting lots of pressure on the stock you can see your heartbeat in the crosshairs, causing the wobble. Try lightening up your shoulder contact and pressure and see if that helps, and it's free.
This and holding the stock in the same manner everytime. Changing hand position and amount of pressure applied on the stock will affect where the bullet goes.
 

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