Use Your Head About Shoulders
If you can't straighten your shoulders when you stretch your arms overhead, you're in for some challenges in yoga. Tight shoulders can make Adho Mukha Vrksasana (Handstand) a battle, compress your low back in Virabhadrasana I (Warrior I), keep your arms bent in Urdhva Dhanurasana (Wheel Pose), and disrupt the beautiful vertical line in simple asanas like Vrksasana (Tree Pose).
But you can make long-term changes in shoulder mobility with regular work on just a few simple poses, and your more challenging asanas will improve noticeably. Several muscles can limit your ability to stretch the arms overhead, but two of the most important are the pectoralis major and latissimus dorsi. The pecs are large chest muscles that originate on the breastbone and collarbones and insert on the outer upper arm bones (humerus). The lats are large, flat muscles on the back, which originate on the pelvis and the mid- and low-back vertebrae. From there, they extend up and diagonally out across the back, wrap through the armpits, and insert on the inner humerus.
If your pecs and lats are short and tight, they strongly limit shoulder flexion, the ability to stretch the arm up. Sometimes these muscles are short because you've worked hard to strengthen them through activities like sports and weight training. Often, however, the tightness is due to lack of stretching. If you only stretch your arms high enough to reach a cup on a shelf or get a comb to the top of your head, your shoulders will maintain just that amount of flexibility. There aren't many activities in daily life that use a full 180 degrees of shoulder flexion, so the average person probably only has 150 degrees, far less than you need for a good Adho Mukha Svanasana (Downward-Facing Dog).
Tight pecs and lats not only limit your ability to fully stretch your arms overhead, they also strongly pull the shoulder into internal rotation. This causes problems in yoga because most asanas require external rotation. To experience external rotation, stand with your arms at your sides and turn the palms forward. If you hold that rotation and bring your arms forward and overhead, the palms will face each other or even point slightly backward. This is the rotation you need in arms-overhead poses like Warrior I, Tree, Handstand, and Headstand. If instead you internally rotate your shoulders and then raise your arms overhead, the elbows tend to bow outward, and you lose important alignment and support in weight-bearing poses like Down Dog, Handstand, Headstand, and Wheel.
Spreading Your Wings
Before we focus on stretching the pecs and lats, let's consider another muscle that can limit full shoulder flexion, the rhomboids. Located between the spine and shoulder blades, these muscles pull the blades toward the spine. As you lift your arms up, either to the sides or to the front, the shoulder blades should broaden away from the spine and rotate upward. If tight rhomboids prevent the scapula (shoulder blade) from moving, your shoulder flexion can be significantly limited.