For a subset E of the BIDISC D2, M={fÎH2(D2) :f=0on E} and N is the orthogonal complement of M in H2(D2) where H2(D2) is the two variable Hardy space on D2. We describe the finite rank commutants of the restricted shifts Sz and Sw on N when E satisfies some natural condition. Moreover we give a sufficient condition for that the Pick interpolation is possible.