A improved flexible annular stapler for joining annular organs (163, 164) is disclosed. The novel stapler features greater accuracy of operation and better control by the operator, as well as additional functions, such as internal illumination (76) and viewing facility (82), and accommodation of a large number of accessories, such as fibroscopes (90) and catheters. The novel stapler features easy attachability of both stapling jaws (18, 25) and easy detachability of the head (11). The novel features of the flexible stapler, and associated methods performed thereby, are particularly useful for closed surgery.