System synchronization is an important technology in constructing all-optical signal processing systems. To realize this, an all-optical timing extraction circuit is required, which recovers timing information from an incoming optical data stream, and produces an optical clock without intermediate electric stage. A potentially simple method of all-optical clock recovery uses self-pulsating laser diodes (SP-LDs), and many experimental studies have been reported so far. However, there is no report on theoretical works to our knowledge except the perturbation analysis by Lee and Shin. In this paper, we report numerical analysis of all- optical clock extraction using the SP-LD based on rate equations. The model used in this analysis is two-section SP-LD. The laser is divided into a gain region (region I) and a saturable absorber region (region II). The carrier lifetime of region II is much shorter than that of region I. THe photon density of injection signal is coherently coupled to the SP-LD light. To obtain the time response of the laser, we solved rate equations numerically. It is shown that we can extract clock pulses from signals which contain regulated digital patterns or a pseudo- random binary sequences (PRBS) data pattern. The results will explain the experimental results reported so far. Relative phase of the extracted clock with respect to the input signal varies when the power of the input optical signal fluctuates or a PRBS data pattern is used. However, this inherent effect can be minimized by using low input power level, although the locking range becomes narrow.