The new simulation model, named SIPSON, based on the Preissmann finite difference method and the conjugate gradient method, is presented in the paper. This model simulates conditions when the hydraulic capacity of a sewer system is exceeded, pipe flow is pressurized, the water flows out from the piped system to the streets, and the inlets cannot capture all the runoff. In the mathematical model, buried structures and pipelines, together with surface channels, make a horizontally and vertically looped network involving a complex interaction of flows. In this paper, special internal boundary conditions related to equivalent inlets are discussed. Procedures are described for the simulation of manhole cover loss, basement flooding, the representation of street geometry, and the distribution of runoff hydrographs between surface and underground networks. All these procedures are built into the simulation model. Relevant issues are illustrated on a set of examples, focusing on specific parameters and comparison with field measurements of flooding of the Motilal ki Chal catchment (Indore, India). Satisfactory agreement of observed and simulated hydrographs and maximum surface flooding levels is obtained. It is concluded that the presented approach is an improvement compared to the standard "virtual reservoir" approach commonly applied in most of the models.