The antiplane problem of the composite wedge consisting of two homogeneous external wedge-shaped areas and an intermediate zone of the interphase is studied. The interphase material is assumed functionally graded. It is shown that the problem in each area is harmonic within the quadratic law of inhomogeneity of the material in the transverse direction. The influence of the interphase on the stress state at the top of the wedge is analyzed. As compared to the ideal contact of external materials, the presence of the interphase leads both to decrease and increase in the singularity exponent. Moreover, the stress asymptotic may have two singular terms for some values of the composite parameters.