The behavior of embedded planar elliptical cracks within square prismatic bars that are commonly used as torqueresisting structural components motivates this work, as the literature for such stress intensity factors is evidently deficient. The stress intensity factors are evaluated using the dual boundary element program of Beasy, and studied by considering the elliptical aspect ratio and the eccentricity in the sense of an offset from the centroid. The variation of shear mode stress intensity factors for a penny crack situated near to the free surface and the square corner is also reported for the first time, complementing the available results for tensile mode.