Mapping functions of various ellipses are gained by complex function theory. Applying stress function with complex variables, a mechanical model of the stress field and the stress components near the hole is presented. The influences of three different geometric parameters of elliptic hole on stress around hole are discussed subject to bending moment. The results show that the length of long axis and short axis is more uniform, the peak stress around hole edge is greater. The work above will provide theory references on choosing hole shape in practical engineering.