By use of complex variable theory, formulae for tangential stress on ellipse edge are derived. Sub-crack point, opening angle and maximal tangential stress on ellipse edge are studied under uniaxial compression, biaxial compression, or uniaxial compression and crack water pressure separately. Based on the maximal tension stress criterion, formulas of maximal tangential stress and critical load are presented. The results show that sub-crack point, opening angle, maximal tangential stress and critical load are varied with different aspect ratio and different inclined angle. Meanwhile, the most dangerous inclined angle is obtained.