Methods and devices which a surgeon may use to stabilize the beating heart during a surgical procedure on the heart. A stabilizing device may be introduced through an opening in the chest and brought into contact with the beating heart. By contacting the heart with the device and by exerting a stabilizing force on the device, the motion of the heart caused by the contraction of the heart muscles in a vicinity of a site of surgery to be performed, is effectively eliminated. A surgeon may contact the heart with the stabilizing means, assess the degree of movement of the anastomosis site, and exert a force on the stabilizing means such that the contraction of the beating heart causes only minimal excess motion at the surgery site. The stabilizing means may be attached to a rigid support or may be attached to a semi-rigid support which is rendered motionless mechanically, chemically, or by human intervention.