Did some reloading for my tang safety Ruger Mod. 77 7mm Remington Mag. Mild load of H4350 to save my shoulder. Target pictured was shot at 100 yards, this A.M. First shot was in the 5 ring, 2nd shot was in the 6 ring and 3rd shot was in the 7 ring. Stiff breeze from my right.
The interval between shots was less than 2 minutes each, so barrel was warm but not hot. I have never seen a string where each round gets progressively LOWER! Barrel is not free floated. Unusual?? Your comments please..

As I was reading your info and seeing the target, I was thinking the barrel was not free floated. If the barrel is making contact with the stock, and you are putting any kind of pressure on the stock, the bullet will go where it wants to go, not where you want it to go. Depending on your set up, it can certainly cause this. Take that same rifle on a bipod, and all bets are off on where it's going.

I used a standard front bag on an adjustable rest. Rifle was able to move vertically since I put no pressure down on rifle. Used a rear bag under the buttstock to adjust elevation. Snugged recoil pad against shoulder.
I have never used a bipod and longest shot I take is usually well under 200 yards.
I am "Old School" Jack O'Conner fan and typically zero my rifles to shoot 3" high at 100 yards .It works for me.

Many 77s have contact at the end of the stock to the barrel. I have in the past taken the appropriate size socket and wrapped it in sand paper to open this channel up.

NOTE: It made a significant difference every time I’ve done it. Usually a positive change, but not always.

Vertical stringing can come from powder charge as well. The old theory was something like vertical stringing more powder. That said I have seen rifles with stock pressure on the fore end walk and keep walking up and off the paper..

What bullet and load?

Just a plain old oily bore can do this. If that would be the case, it would settle down after a few rounds.

FWIW, My powder charge was EXACTLY the same on every cartridge. I have plenty of time to make sure that each case is exactly the same length and weigh each bullet to make sure that everything is as uniform as I can possibly make it.
Also, the bore was not oily, I leave the bores fouled on my rifles.
My load was 57 grs. of H4350, Sierra 150 gr. Spitzer Boattail..
As you can see from the picture attached, my load was a full 2 grains LOWER than the load recommended by Hodgdon.

Check the action screws. Front angled screw should be Gorilla tight. Ruger recommends 90 inch pounds. Rear screw somewhere around 30-35 inch pounds. Ruger 77’s I have owned are finicky about the action screws. I own a LH 270 MK II that I sanded the pressure band out of the fore end and bedded the action before I could get it shooting. It is MOA with hand loads but not what I would call a tack driver. I burned a lot of components getting it to that point.

I will put money on it that's it's not ammo or powder related at all. It is the contact and pressure point from the stock on the barrel or a stock to action mating issue that is causing a POI shift. I have seen this many many times. I have been given high end custom rifles that were high dollar builds, and would shoot like crap and string just like this. There was pressure on the barrel from the stock in some form, or the stock was not fitted or bedded properly. I would free float the barrel or fix the stock/action pressure issue and the rifle would become a tack driver that shot very consistent. With what I do with custom load work ups and such, I see a lot of what I call, "Problem Rifles", and I know what to look for and often know what causes certain issues. Bolt guns should not have contact on the barrels, in any form. The free floating of the barrel allows it to have consistent harmonics for every shot. And if the stock is not fitted correctly to the action, then you get weird pressure points that cause stringing. It will be one of these 2 items causing the stringing.

If you have loaded for this rifle before, did it do this? If no does it do this with those loads now?

Chad, I agree with what you say but the way the rifle strings is what has me baffled. I have read (and been told) that a rifle tends to recoil AWAY from the point that the barrel touches the stock.
I.E. pressure band is at the front of the stock so rifle should shoot high. Mine shoots LOWER with each shot??
I am not using a lead sled and I exert no pressure down on the stock fore end at all. When the rifle recoils it moves UP away from the leather front rest.
The action screws are tight. I have free floated the barrel for the next range trip.

Wood rifles are strange sometimes. I’ve seen pressure points just in front of the recoil lug area that the stock sets on. When a barrel heats up, it can move whatever direction it wants. Most of the time they do string up and down. There are ways to check for stress points in the bedding/stock mating to the action.

Kmon: These loads are different from what I loaded previously. As noted, I reduced the loads to achieve less recoil. I have some factory ammo and other reloads that are quite a bit hotter.and are NOT comfortable to shoot.
I do not own a chronograph, but I estimate the muzzle velocity at about 2800 fps.

Trick i learned from my grandfather. If gun won't shoot before you make permanent free float changes. Take a old credit card cut it to fit under the barrel lug in the stock. Put it back together barrel should be free floated. Shoot it and see if its worth it. I've got rifles I just left the cc in.

Free floated barrel...done!