Abstract: The complex variable function method is an effective method for solving plane elasticity and defect problems. In this paper, the complex variable function method for classical theory of elasticity is developed to that of the quasicrystals. Elastic fields of the decagonal quasicrystal subjected to a line force as well as its dislocation are investigated. The representations of stresses and displacements are developed in terms of four analytic functions. The real form solutions are obtained by solving the system of equations derived from the boundary value problem considered. The analytic expression of the elastic energy is obtained. The effect of phonon-phason coupling elastic constants on the mechanical behavior is also discussed.