The one-parameter singular expression for stresses and displacements near a crack tip has been widely thought to be sufficiently accurate over a reasonable re ion for any geometry and loading conditions. In many cases, however subsequent terms of the series expansion are quantitatively significant, and so we now consider the evaluation of such terms and their effect on the predicted crack growth direction. For this purpose the problem of a cracked orthotropic plate subjected to a biaxial load is analysed. It is assumed that the material is ideal homogeneous anisotropic. BY considering the effect of the load applied parallel to the plane of the crack, the distribution of stresses and displacements at the crack tip is reanalyzed. In order to determine values for the angle of initial crack extension we employ the normal stress ratio criterion.