3k87 is a math-coprocessor which is pin-to-pin compatible with 80387 having more than 300,000 transistors. So design for testability is important to reduce the cost of testing and diagnosis. Built-in self test was adopted to test regular structured circuits, such as PLA or ROM. The basic concepts used in applying BIST to 3k87 and details of design of BIST circuits are described in this thesis. BIST in 3k86 has some features which reduce hardware cost and locate fault. Circuits used in 3k87 BIST can be generated automatically. Fault simulator developed for obtaining the polynomial of the signature register which detects as many faults as possible and for analyzing BIST circuits is introduced.