Horizontal pulling develops the trapezius, latissimus dorsi, biceps and forearms.
Due to the complexity of the upper back muscles, I recommend including both chin ups and a horizontal pulling exercise in the Elastic Strength program.
Chin ups are the best vertical pulling multi-joint exercise for the latissimus dorsi and biceps, but they do not properly load the trapezius function of scapular retraction. To properly train the trapezius you need inverted rowing or fulcrum 90º pull ups to the sternum.
Inverted rowing is easier than 90º pull ups to the sternum, so many people will have to use this exercise when they start the Elastic Strength program.
Inverted rowing is safer than rowing with barbell because you do not bend over at the waist, removing strain from the lower back.
Inverted rowing involves the shoulder girdle in keeping the body parallel to the ground, as in a front lever. This results in greater upper back activation IF you use adequate resistance.
Inverted rowing should be done using a supinated or neutral grip.
If using a single bar, use a supinated grip. This puts the biceps in their strongest pulling position so they do not limit the load you can put on the upper back. Bret Contreras found that the supinated (underhand) grip inverted row with feet elevated produced one of the three greatest peak lat activations.
If you have rings or a suspension trainer you can use a neutral grip or what I find most comfortable, a neutral grip in the bottom position (arms extended) and active supination as you pull into the contracted position.
You can adjust the difficulty of inverted rowing easier by changing the height of the rings or bar. A higher bar/rings set up makes the movement easier.
Assuming the table position (knees bent) so the lever arm is shorter also makes it easier.
You progress by lowering the bar or straightening the legs, then progressively raising the legs so that your body is parallel to the floor in the extended position.
Once you can do the inverted row with the feet elevated you can progressively load the inverted row by using two Cartman tie down straps tied together, loaded with barbell plates which are secured to the straps by carabiners which prevent the plates from sliding off the straps. You then lay the straps across your abdomen with plates evenly distributed on each side of your body.
When you are strong enough to do inverted rowing with feet elevated you may be able to do fulcrum 90º pull ups a.k.a. sternum pull ups.
If you can scale fulcrum 90º pull ups to your ability, you should do these rather than inverted rowing in the Elastic Strength program.
These improve on inverted rowing by enabling you to work the upper back through a greater range of motion. I have written a whole article on fulcrum 90º sternum pull ups explaining why they are probably the best single upper back exercise, combining the movements in pull up, pull over, and rowing into one awesome exercise.
You can progress the load by the same method I described above for the inverted row. Eventually you will be able to do 90º pull ups without your feet resting on a bench.
If you can't do fulcrum 90º pull ups yet, do inverted rowing until you can.
If you can do fulcrum 90º pull ups, they should be your staple for horizontal pulling until you can do 90º pull ups without your feet supported.