There are many exercises that can be done to increase the range of motion and flexibilty of the shoulders. Many of these execises can also strengthen the shoulders. The most effective range of motion shoulder exercise and strengthening exercises is what I cal the tri-lateral exercise because it will increase the productivity of all the parts of your shoulders.
TRI-LATERALS Shoulder exercise
Start from the seated position or standing. Begin the 1st motion of the exercise with your arms straightdown the sides of your body (meaning your arms and hands must be alongside your body with your finger toward the ground. From this stance you will then in a steady motion lift your arms and hands above your head point toward the sky. Once they are fully extended and parallel again steadily bring them back down to your sides completely. Repeat this motion at a steady pace. Go faster to burn fat or slower to build strength. You should look like you're trying to fly.
Hold your arms straight out and fully extended to the width of your wing span, and parallel with your shoulders. From there you will bring them together util your hands touch. Your arms must remain fully extended. Once your hands touch do the motion backwards. Repeat at a steady pace.
Start your arms from the same position as step 2, straight out fully extended and parallel with your shoulders. From this position with your arms slightly stiffened you will make small circles by twirling your arms clockwise at a steady pace. As you go along you will increase the size of the circles creating more resistance and increasing the range of motion.
Systematically move from step 1 to 3 in any order, working all the parts of your shoulders.
Increasing your range of motion as you progress.