Flow birefringence induced in dilute solutions of poly[(1,4-naphthylene)-2,5-diyl-1,3,4-oxadiazole] and poly[2,6-naphthylene)-2,5-diyl-1,3,4-oxadiazole] in conc, sulphuric acid has been investigated. The shear optical coefficient was found for these polymers to be approximately double the value of that obtained in the same solvent for poly[( para-phenylene)-2,5-diyl-1,3,4-oxadiazole]. Rigid-chain behaviour of the polymers was characterized by hydrodynamic and dynamo-optical parameters evaluated with application of the worm-like chain model and the “method of similar structures”. Change in optical anisotropy of a chain unit induced by incorporation of naphthylene groups into the main chain has been evaluated.