I think it'll depend upon whether one is talking about physical or emotional pain, but assuming you are talking about emotional pain I have heard it described as a deep ache, smothering, heaviness, etc. It is interesting (to me) that both physical and emotional pain uses the same neural pathways in the brain explaining why during periods of intense emotional pain one can feel physical pain in the chest or abdomen - hence the terms 'gut-wrenching' or 'heartache'.