The effective electrical conductivity of a two-phase material consisting of a lattice of identical spheroidal inclusions in a continuous matrix is determined analytically. The inclusions are located at the node points of asimple-cubic lattice and the axis of rotation of each spheroid coincideswith one of the lattice vectors, such that the spheroids are aligned witheach other and with the lattice. With an electric field applied in thedirection of the rotation axes of the spheroids, the electric potential isfound by solving Laplace's equation. The solution is found by analyticallycontinuing the interstitial field into the particle domain and replacing theparticles with singular multipole source distributions. This yields anexpression for the potential in the interstitial domain as a multipoleexpansion. Using Green's theorem, it can be shown that only the firstcoefficient in this expansion is required to determine the effectiveconductivity of the composite. The coefficients are determined by applyingcontinuity conditions at the particle-matrix boundary and, in a novelapproach, this is achieved by transforming the multipole expansion into anexpansion in spheroidal harmonics. Results for spheres and prolate andoblate spheroids are compared with experimental data and previoustheoretical work, and excellent agreement is observed.