In response to the defects in the right-angled domain, this paper conducts a theoretical study on the variation of the concentrated stress at the edge of an elliptical hole in this domain. Firstly, the iterative mirror image method is employed to transform the right-angled domain space into the full space. By using the polar coordinate transformation method, the expressions of the mirrored elliptical hole in the original complex-plane coordinate system are derived. Secondly, the stress expressions are deduced by using the Hankel wave function combined with the complex variable function. Then, with the help of the elliptical hole equation, the relationship between the argument of a point on the elliptical edge and the angle between the perpendicular line of this point and the coordinate axis is established, thus avoiding the use of the traditional conformal transformation method. Based on the free-stress boundary conditions of the elliptical hole edge, an infinite system of linear algebraic equations is established. Finally, a finite number of terms are intercepted to solve the unknown coefficients. Through the analysis of the distance between the center of the elliptical hole and the upper and right boundaries, the incident angle, the deflection angle of the elliptical hole, and the incident wave number, the following conclusions are obtained: the larger the incident wave number, the higher the fluctuation frequency of the dynamic stress concentration factor; when the incident wave is at a low frequency, as the distance from the right boundary increases, the dynamic stress concentration factor first decreases and then tends to be stable, and the stable value of the distance is 5. This research provides numerical conclusions for the dynamic stress factor at the edge of elliptical defects in the right-angled domain and offers detailed theoretical results for the defect detection of right-angled plates in practical engineering.