The role of the shoulder strap is to ensure that the cup is close to the chest. The straps should not dig into the shoulder or sit too loosely and fall down. If the straps dig in, it may be because they are too narrow and don't give sufficient support. Shoulder straps that are a little wider and are lightly padded will put less strain on the shoulders, giving you maximum support from your bra.
Try a bra with wide padded shoulder straps that lift and support your bust!