There are numerous reasons for a rounding of the upper spine. If you are developing kyphosis, commonly called “dowager’s hump” when it develops later in life, I'd recommend seeing your doctor to determine the cause and develop a treatment plan, which might include strength training. If it's a matter of improving one's posture, strengthening the back muscles can really help, along with increasing the flexibility of the chest muscles. But to put those muscles to good use, we still need to remind ourselves, often, to stand or sit up straight!
From the Mayo Clinic:
“Kyphosis treatment depends on the cause of the condition and the signs and symptoms that are present.
Less serious cases:
In some cases, less aggressive types of treatment are appropriate:
• Postural kyphosis. This type of kyphosis doesn't progress and may improve on its own. Exercises to strengthen back muscles, training in using correct posture and sleeping on a firm bed may help. Pain relievers may help ease discomfort if exercise and physical therapies aren't fully effective.
• Structural kyphosis. For kyphosis caused by spinal abnormalities, treatment typically depends on your age and sex, the severity of your symptoms and how rigid the curve in your spine is. With Scheuermann's kyphosis, monitoring for progression of the curvature may be all that's recommended if you have no symptoms. Anti-inflammatory medications may help relieve pain. General conditioning exercises and physical therapy may help alleviate symptoms.
• Osteoporosis-related kyphosis. Multiple compression fractures in people who have low bone density can lead to abnormal curvature of the spine. If no pain or other complications are present, treatment for the kyphosis may not be necessary. But your doctor may recommend treatment of the osteoporosis to prevent further fractures and worsening of the kyphosis." Read more at Mayo Clinic.