The causes of dull aching pain under left breast radiating to back, is often taken as a sign of heart attack. However, there is another form of chest pain known as Angina is that is caused by unwarranted physical exertion or stress on the back side. Another cause could be muscle spasm or pinch in or around both sides of the ribs. You will need to visit a heart specialist for proper diagnosis and treatment. For more information, visit http://www.buzzle.com/articles/pain-under-left-breast.html.