In order to investigate the properties of three-dimensional metallic photonic crystals, we have developed an adaptation of Harrington's method for scattering by thin wires. Due to the peculiarity of photonic crystals, we have been led to renounce to two assumptions: the current intensity in the wires is not assumed to vanish at a free extremity of a wire and the Kirchhoff law at a junction between wires is not used any longer. It is shown that, paradoxically, the numerical implementation is simplified by these changes and that our method provides a better convergence of the results. Using our code, the properties of 3D metallic photonic crystals are investigated and compared with those of 2D crystals.