A vein harvesting assembly for harvesting a vein in a body comprises: a dissecting member, with the dissecting member being insertable into the body and moved along a vein to dissect tissue surrounding the vein. A covering member possesses a proximal end portion and a distal end portion, with the covering member possessing a covered space extending from the proximal end portion to the distal end portion, and the covering member being mountable on and movable along the dissecting member when the dissecting member is positioned in a living body. A cutting member is comprised of an elongated member and a blade member so that rotation of the elongated member results in turning of the cutting member to cut tissue surrounding the vein. The cutting member is insertable into the space in the covering member and is movable in a distal direction along the space.