Weight lifting to help off hand shooting

A great exercise for handguns is to attach some heavy twine to a suitable Rod (broomstick, closet rod) and weight at the opposite end, extend the rod in front of your chest with both hands, and then roll the weight from the floor to your hands and back again, alternate clockwise and counter clockwise. A 1lb weight will get old pretty quick, it really strengthens the wrists.

Of course it's always good to do some muscle strengthening exercise, but in my book it's not "how still you can hold a gun" but "timing" is!
By that I mean that (unless you are a very trained competition shooter, with thousands of practice hours) you are always going to have some motion of the crosshairs/frontsight or whatever aiming device you use while shooting off hand. The trick here is to accept that, and not fight it, but trying to grasp the direction of motion in relation to the target, so as to let off the shot when the reticle will be smack on the bullseye. The proof of this philosophy lies in the "instinctive shooting" training that was developed decades ago in the US military. They would throw up some bottlecap size targets up in the sky, and each private was to swing their gun onto them and hit as many as possible. After only just a few hours of practice most of the soldiers were able to hit multiple targets in one go!

By concentrating on this technique of timing when the aiming device and the target will intersect you get a much faster and much more satisfiyng result than when trying to keep the gun still IMO.

Technique and choice of rifle is important for me when it comes to off-hand shooting. If the rifle and scope are too heavy for you or poorly balanced then your arm will be shake. 

I use an unorthodox off-hand technique that works fairly well for me. I use my forearm, just in front of my elbow as a rest. It gives me much better stability than trying to rest the forend on my hand.

I agree 100% about strengthening the muscles used for off-hand shooting. If you can do this in the gym as part of your workout, that's probably quickest. Getting plenty of practice until you get used to the weight of your rifle is a close second. 

Deltoids are most important for my grip.

It highly depends on what deiscipline you are shooting. For static match off-hand shooting the simplest and probably the most effective excersize is holding a rifle in a correct aimed position for 5-10minutes, aiming down the sigts. Then slowly following the stright horizontal and vertical lines down the sights by turning your torso, remaining in a correct position. Muscles used while doing a static off-hand shooting are barely used in a normal everyday life, so even 10 minutes of standing still while aiming down the sights is a challenge for most people, even for those in a very good physical shape. The final goal is overall balance and stability of the shooting position, so you want not only to inure those muscles to withstand static loads caused by hoding a rifle, but also to get a feel of what is the balanced stable position and to develop a habbit to intuitively assume it each time you shoulder a rifle. So the next step is the same static excersize, but performed standing on a quite narrow square shaped wooden log. If you want to go even further, you can add wights to the barrel with time.

It must be kept in mind though, that excessive excersizing in off-hand position is not good for your health, especially your spine. So these excersizes and off-hand shooting sessions must be followed by other excersizes aimed and relieving the stress to the spine.

iride with those specs you would be able to toss me around like a sail cat on a string.

Thurmond

Shot a squirrel at about 25 yards today. Dog was barking at it and the squirrel was barking at the dog from about 20ft up the tree. Pulled up the WC and when the cross hairs were on the squirrel ... pulled the trigger. DRT. Through and through. If I had stood there for even ten seconds thinking about it I would just as likely have missed. I've always been a snap shooter. If I think about it my percentage goes out the window. Same with skeet. Never put the gun to my shoulder till the clay is in the air. I do ok that way.

Shot a pig at 200 yards from my front porch ( 270 Winchester ) sitting at a table with front and rear sand bags yesterday and pulled the shot. Killed the pig but very sloppy. I got excited as the pig was just about to duck back in the brush and crunched the trigger. The second I did it I wanted to slap myself. Nice thing about airguns you are so much less likely to flinch as you know there is no recoil and little report. I'm a much better shot with an airgun than a powder burner.

I am also a free pistol shooter. A fellow competitor started weight lifting. I assumed it would help his shooting. As he bulked up, his scores went down. He said he thought it was a detriment to his fine motor skills. I don't often see muscle bound free pistol or air pistol shooters on the podium.

As brent375hh points out bulk muscles are not wanted in slow deliberate shooting. Fast twitch muscles (those with bulk) move too rapidly, but are great for moving heavy weights. What you want to do is balance and slow movement exercises like yoga and Tai Chi. Instead of lifting heavy weights rapidly a few times (as is the process for strength training), very slow controlled motions with light weights is much more productive for this sport.