A formal multipole expansion of tensor functions dependent onseveral vector parameters is obtained in an invariantdifferential form. We apply this result to derive multipoleexpansions of finite rotation matrices in terms of finite sumsof bipolar harmonics. The multipole expansion in terms ofbipolar harmonics of unit vectors r̂1 and r̂2are analysed for functions of the type f(r)Ylm(r̂)(with r = r1-r2), which are important intwo-centre problems. As another example of the application ofthe multipole expansion technique, reduction formulae areobtained for tensor constructions which appear in analyses ofangular distributions in photoprocesses which take exact accountof non-dipole (or retardation) effects. As a result, the`photon factors' in the angular distribution for an arbitraryphotoprocess are expressed in an invariant form involving onlythe photon polarization vector and spherical harmonics of thephoton wavevector.