A brittle coating stress analysis technique applicable to orthotropic materials has been developed. The technique has been applied to a unidirectional glass fibre reinforced epoxy. Its behaviour has been studied under uniaxial and biaxial stress fields using cantilever beam specimens and circular disc specimens under diametral compression. Fibre orientation in the specimens has been varied. In each case it has been observed that the cracks represent the direction of principal strains in the specimen material and not the direction of principal stresses. It is also observed that the threshold strain in the coating is not affected by the biaxiality of the stresses in the coating.