We propose a numerical technique for modeling quantum multimodal light scattering by a perfectly conducting body. Using the special quantization technique, we develop the quantum adaptation of the characteristic mode approach widely used in classical electrodynamics. The method is universal with respect to the body's configuration, as well as its dimensions relative to the wavelength. Using this method and calculating the first- and second-order field correlation functions, we demonstrate how scattering affects quantum-statistical features of the field. As an example, we consider the scattering of two single-photon incident Gaussian beams on a cylinder with a circular cross section. We show that the scattering is accompanied by two-photon interference and demonstrates the Hong-Ou-Mandel effect. It is shown that the scattered two-photon field and its correlations manifest directive propagation, which is controllable by various means (angles of incidence, configuration of the body, relations between its dimensions and the wavelength). We expect that this method will be useful for designing quantum-optical devices.