In this paper we consider the problem of determining the stresses of a bi-material plate with an elliptical hole by a finite-element numerical method using the Freefem++ package. The plate is formed by joining two half-planes of different materials, the hole is located entirely in the lower half-plane. The constant stresses are given at infinity. The stresses on the interface are calculated for various elasticity parameters of the half-planes, different distances of the center of the ellipse from the interface, and also the orientation of the ellipse in the plane. The numerical results are compared with the solution obtained by the analytical method. Also, the stresses on the contour of the elliptical hole are calculated.