Context. The coded-mask spectrometer-telescope SPI on board the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) records photons in the energy range between 20 and 8000 keV. A robust and versatile method for modelling the dominating instrumental background radiation is difficult to establish for such a telescope in the rapidly changing space environment. Aims. In a previous paper we presented our spectral parameter database, developed from long-term monitoring of the SPI germanium detectors, that characterises the instrument response and background behaviour. Our aim is to build a self-consistent and broadly applicable background model for typical science cases of INTEGRAL/SPI based on this database. Methods. The general analysis method for SPI relies on distinguishing between illumination patterns on the 19-element germanium detector array from background and sky in a maximum-likelihood framework. We illustrate how the complete set of measurements, even including the exposures of the sources of interest, can be used to define a background model. The observation strategy of INTEGRAL makes it possible to determine individual background components, originating from continuum and γ-ray line emission. We apply our method to different science cases, including point-like, diffuse, continuum, and line emission, and evaluate the adequacy in each case. Results. From likelihood values and the number of fitted parameters, we determine how strong the impact of the unknown background variability is. We find that the number of fitted parameters, i.e. how often the background has to be re-normalised, depends on the emission type (diffuse with many observations over a large sky region, or point-like with concentrated exposure around one source), the spectral energy range, and bandwidth. A unique timescale, valid for all analysis issues, is not applicable for INTEGRAL/SPI, but must and can be inferred from the chosen data set. Conclusions. We conclude that our background modelling method can be used in a wide variety of INTEGRAL/SPI science cases, and provides nearly systematics-free and robust results.