Pressure on the chest can indicate cardiac/heart problems. Chest 'pain' is not necessarily felt as 'pain' but can be described as tightness or pressure on the chest and can radiate to the neck, jaw, arm ( especially left arm) or back. It can also be accompanied with sweating and nausea. This can be caused by lack of oxygen to the heart and lead to a heart attack. Chest pressure caused be lack of oxygen can be noticed with activity and then relieved with rest. This is something that can be very serious and needs to be evaluated by a physician right away.