In this work we analyze the effect of hydrodynamic interaction (HI) on diffusion-controlled reaction rate of molecules with highly anisotropic reactivity, modeled by small reactive hemispheres around the reactive centers (RCs) on the surfaces of molecules. The effect of the HI (that manifests itself in the coordinate dependence of relative diffusion coefficients) is shown to be mainly determined by the HI at short distances between molecules (where the traditional long distance analysis of the HI is irrelevant) and very sensitive to the local shape of molecules near the RCs. The effect is analyzed within three models of the shape: spherical, non-spherical spheroidal, and non-spherical of truncated-sphere type, with the use of the method of local analysis based on the approximation of the general curvilinear coordinates of pairs of reacting molecules by the Cartesian ones in the region close to the reactive orientations. Simple analytical expressions for the reaction rate are derived, which show that the HI effect can manifest itself in fairly strong (about 3-5 times and larger) reduction of the rate. (C) 2003 American Institute of Physics.