Abstract:By introducing the generalized conformal transformation and using the complex variable function method , the analytic solution of the plane elasticity problem of elliptical hole in one-dinensional orthorhombic quasicrystals were obtained and derived complex repesentation of stress displacement . In some special conditions,the elliptical hole can be turned into a Griffith crack and the SIFs of crack tips can be obtained. The plane elasticity problem of elliptical hole in 1D orthorhombic QCs could extended for 1D tetragonal QCs and the analytic solution of plane elasticity problem of elliptical hole in 1D tetragonal QCs. The elliptical hole can be also turned into a Griffith crack in specical conditions and the SIFs also be obtained.