An analytical solution is presented for the electrical conductivity of a material composed of spheroidal particles embedded in a matrix. The particles are arranged on a simple-cubic lattice with their axes of rotation aligned with one of the lattice vectors. In this arrangement, there are two independent components of the conductivity tensor; one for the electric field applied parallel to the rotation axis of the spheroids and one for the electric field applied perpendicular to this axis. Both components are calculated using a method in which each particle is replaced by a singular multipole source which gives rise to the electric potential in the interstitial domain. This potential can readily be written as a sum of spherical harmonics but, in order to treat spheroidal particles, it is necessary to transform the solution into one in terms of spheroidal harmonics. The calculation of the matrix elements required for this transformation is described and the solution for each component of the conductivity tensor is given in analytic form. Results are presented for various values of particle aspect ratio, volume fraction and conductivity ratio between the two phases. Very good agreement is observed with experimental data and the results of an independent calculation.