The characteristics of the Solid-state Neutron Detector, under development for neutron-scattering measurements at the European Spallation Source, have been simulated with a Geant4-based computer code. The code models the interactions of thermal neutrons and ionising radiation in the 6 Li-doped scintillating glass of the detector, the production of scintillation light and the transport of optical, scintillation photons through the the scintillator, en route to the photocathode of the attached multi-anode photomultiplier. Factors which affect the optical-photon transport, such as surface finish, pixelation of the glass sheet, provision of a front reflector and optical coupling media are compared. Predictions of the detector response are compared with measurements made with neutron and gamma-ray sources, a collimated alpha source and finely collimated beams of 2.5 MeV protons and deuterons.