Methods and devices used to stabilize a beating heart during a surgical procedure on the heart and to expose a surgical site are disclosed. The stabilizing device is introduced through an opening through the chest and brought into contact with the beating heart, and by exerting a stabilizing force on the device, the motion of the heart caused by the contractions of the heart muscles is effectively eliminated. Exposure members are actuable to reposition a portion of the surface of the heart to better expose a target artery or other surgical site. Accordingly, the heart is stabilized and movement of the site of the surgery is minimized. Typically, in separate steps, a surgeon contacts the heart with the stabilizing device, assesses the degree of movement of the anastomosis site, and exerts a force with a stabilizing device such that the contractions of the beating heart causes only minimal excess motion at the surgery site, whereupon exposure members further reposition heart tissue to better expose the surgical site. The stabilizing device 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.