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This paper derives a general procedure to produce an asymptotic expansion for eigenvalues of the Stokes problem by mixed finite elements. By means of integral expansion technique, the asymptotic error expansions for the approximations of the Stokes eigenvalue problem by Bernadi–Raugel element and Q₂-P₁ element are given. Based on such expansions, the extrapolation technique is applied to improve the accuracy of the approximations.