Abstract Periodic solutions are derived for the one-velocity transport equation in an infinite two-dimensional lattice of absorption lines in a moderating medium. The angular distribution of scattering is given by a truncated Legendre series. The unit cell of the lattice may be an arbitrary parallelogram so that the most common reactor lattices (square, hexagonal, triangular) are included as particular cases. The angular flux is expanded in a double Fourier series over the primitive cell. The coefficients are functions of the angular variable and can be expressed in terms of their spherical moments, which in turn, are solutions of a system of algebraic equations whose order is determined by the length of the truncated Legendre series. The terms of the double Fourier series exhibit an asymptotic behaviour of the type ( m 2 + n 2) − 1 2 , and are therefore only conditionally convergent. The solutions possess a 1 r singularity at the location of the absorption lines.