Programmable memory built-in self-test (PMBIST) is an attractive approach for testing embedded memory. However, the main difficulties of the previous works are the large area overhead and low flexibility. To overcome these problems, a new flexible PMBIST (FPMBIST) architecture that can test both single-port memory and dual-port memory using various test algorithms is proposed. In the FPMBIST, a new instruction set is developed to minimize the FPMBIST area overhead and to maximize the flexibility. In addition, FPMBIST includes a diagnostic scheme that can improve the yield by supporting three types of diagnostic methods for repair and diagnosis. The experiment results show that the proposed FPMBIST has small area overhead despite the fact that it supports various test algorithms, thus having high flexibility.