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Satisfying equilibrium and compatibility equations in an elasticity medium when the body forces don't exist, results the biharmonic equation in domain. U is Airy stress functions so that from derivatives of U one can obtain field stress and strain. Finding U in field real functions for region with general boundary condition is very difficult. But in field complex functions it's possible to compute the general solution of biharmonic equation by two analytic functions obtained so that the boundary value of problem be satisfied on the boundary of region. In this paper solving a multiply connected domain including a plate with circular holes by using complex functions
is verified. Since existing methods for solving this problem are based on the numerical method it is tried to find an
analytic method. For this work the self consistent method in elasticity medium is used and at the end by writing a program with mathematica language some different medium are solved.