If a thin oblique plate (i.e. in the shape of a parallelogram) is subjected to a uniform shear stress parallel and perpendicular to two of the sides, the critical value of the stress depends on the direction in which it is applied. The higher critical value is obtained when the shear is tending to decrease the obliquity of the plate. The ratio between the two critical shear stresses lies between 1 and 8 for a simply supported 45 deg. oblique plate and between 1 and 2·69 for a clamped 45 deg. oblique plate. This paper discusses the phenomenon for 45 deg. oblique plates and shows that even for plates of practical proportions the ratio between the two critical shear stresses may be of the order of 4 if the edges are simply supported.