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The stability of the laminar flat plate boundary layer is investigated numerically by solving the linear Orr-Sommerfeld equations for the disturbulence amplitude function. These equations include the terms of viscosity, density stratification, and diffusion. Neutral stability curve and the critical Re numbers are computed for various Richardson (Ri) numbers and Schmidt (Sc) numbers. The results show that the larger the Ri, the larger the critical Re for Sc ＜ 10. The flow is stable for Ri ＜ 0, when Sc is very small or the mass diffusion coefficient is very large. But for Ri ＞ 0, the effects of diffusion are reversed for Sc ＜ 10. For Sc ＞ 10, the critical Re rapidly decreases to zero as the Sc increases for a given Ri number. The critical Re rapidly decreases as the Ri increases.