Abstract: Using the complex variable function method and the technique of conformalmapping which transforms the complicated region in physical planeonto the interior of the unit circle in \zeta plane, then based on Cauchy integral theory, the plane elasticity problem of anelliptical hole with two straight cracks is solved, and the analyticsolutions of the stress intensity factors for mode Iand mode II problems are obtained. Under the limiting conditions, the present results are reduced tothe results of the well-known Griffith cracks. Moreover, they include the cross crack and the circular hole withtwo straight cracks. Analytic solutions obtained in thispaper are useful in materials science and engineering.