Abstract: Choosing a new displacement potential function and using a half-inverse method and an undetermined coefficient method, the problem about one-dimensional orthorhombic quasi-crystals with an elliptical hole in parallel to the quasi-periodic direction is investigated, the explicit analytical solutions in stress field is given. Under the limiting conditions, the problem of an elliptical hole degenerates into the problem of a Griffith crack. The explicit analytical solutions in stress field and the stress field intensity factor are obtained corresponding to the crack problem.