The plane stress and displacement field around the elliptical hole of an anisotropic linear elastic plate under arbitary orientation of tension force and fibres is analytically determined by the method of stress functions of a complex variable. For this purpose the infinite plate under uniaxial tension is used as mathematical model. For the example of glass fibre reinforced plastics with orthotropic properties it is shown that the data gathered from isotropic materials on the behaviour of stress and displacement around elliptical and circular holes are not applicable to anisotropic materials. This is especially true when load and orthotropic principal directions (off-axis-load) diverge. For several particular cases, the hole stress concentration factors which are decisive for the design are depicted in polar diagrams. The position of the maximum stress is also given which - in contrast to isotropic materials - generally no longer coincides with the notch base.