Compression plate apparatus enables vessels to be joined together in various anastomosis configurations. The compression plates have locking components such as snap-fit components to maintain the plates together. The compression plate apparatus may be utilized with an intraluminally directed anvil apparatus or an eternally positioned anvil apparatus. One of the compression plates assists in the eversion of the anastomosis fenestra contour. One of the compression plates enables a graft vessel to be pre-everted so that the anastomosis fenestra contours are everted. The appparatus provides a structure that enables the vessels to be joined without being penetrated.