A model on the coexisting phase of quasicrystal-crystal is proposed,with which we concretely investigate the interface effects for coexisting phases of one-dimensional orthorhombic quasicrystal-isotropic crystal and three-dimensional icosahedral quasicrystal-cubic crystal.The phason strain fields which play an important role in some processes are determined.Some factors affecting the strain fields,e.g.,the material constants of phonon,phason,phonon-phason coupling of the quasicrystal and the elastic modulus...