The invention is surgical instruments which facilitate substantially linear incisions, especially through the wall of vessels, such as arteries, which have been specifically designed for coronary artery bypass graft procedures (CABG) on the beating heart. The instruments of the invention are particularly useful to create the incision in the artery to which the bypass graft is sewed, typically the left anterior descending artery (LAD). The instruments of the invention allow incisions to be rapidly made, precisely measured, and cleanly formed so that a bypass graft can be rapidly sewn in place. In one embodiment, the invention is comprised of a hand-held instrument with a curved cutting edge formed on the interior edge of a curved or arcuitous segment located near the end of the instrument. The tip of the instrument has a point of penetrating the vessel wall. The point may have several alternate shapes to facilitate penetration of the vessel wall while maximizing the trauma to the surrounding tissue. Another embodiment is comprised of a hand-held instrument with moveable member such that the incision is created by engaging a cutting blade against a stop with the tissue being cut therebetween. This instrument is also constructed to facilitate a rapid linear incisions in a vessel while minimizing the possibility for damage to the surrounding tissue. In another embodiment, the instrument features a motion-cancelling member which compensates for the movement of the target surface to be incised. This embodiment has a cutting blade which is manipulated form handle which is isolated from the movement of the tissue containing or proximate to the target of the incision. The instruments facilitate the invasive cardiac procedures by creating linear incisions quickly without undue trauma to surrounding tissue and without excess loss of blood.