Compression plate apparatus enables vessels to be joined together in various anastomosis configurations. The compression plates are guided to each other in a parallel orientation by guides. The compression plate apparatus may be utilized with an intraluminally directed anvil apparatus or an externally 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 apparatus provides a structure that enables the vessels to be joined without being penetrated.