The linear stability of the triangular points was studied for the Robes restricted three-body problem when the bigger primary (rigid shell) is oblate spheroid and the second primary is radiating. The critical mass obtained depends on the oblateness of the rigid shell and radiation of the second primary as well as the density parameter k. The stability of the triangular points depends largely on the values of k. The destabilizing tendencies of the oblateness and radiation factors were enhanced when k > 0 and weakened for k < 0.