Context. In X-ray observations, estimating the particle-induced background is important, especially for faint and/or diffuse sources. Although software exists to generate total (sky and detector) background data suitable for a given Chandra ACIS observation, no public software exists to model the particle-induced background separately. Aims. We aimed to understand the spatial and temporal variations of the particle-induced background of Chandra ACIS obtained in the two data modes, VFAINT and FAINT. Methods. Observations performed with ACIS in the stowed position shielded from the sky and the Chandra Deep Field South data sets were used. The spectra were modeled with a combination of the instrumental lines of Al, Si, Ni, and Au and continuum components. The spatial variations of the spectral shapes were modeled by dividing each CCD into 32 regions in the CHIPY direction. The temporal variations of the spectral shapes were modeled using all the individual ACIS-stowed observations. Results. Similar spatial variations of the spectral shapes were found in VFAINT and FAINT data, which are mainly due to the inappropriate correction of charge transfer inefficiency for events that convert in the frame-store regions. The temporal variation of the spectral hardness ratio is ∼ 10% maximum, which seems to be largely due to solar activity. We modeled this variation by modifying the spectral hardnesses according to the total count rate. Incorporating these properties, we developed a tool, mkacispback, to generate the particle-induced background spectral model corresponding to an arbitrary celestial observation. As an example application, we used the background spectrum produced by the mkacispback tool in an analysis of the unresolved cosmic X-ray background in the CDF-S observations. We found intensities of 3.10 (2.98-3.21) × 10 −12 erg s −1 cm −2 deg −2 in the 2-8 keV band and 8.35 (8.00-8.70) × 10 −12 erg s −1 cm −2 deg −2 in the 1-2 keV band, which are consistent with or lower than previous estimates. Conclusions. We modeled the spatial and temporal variations of the particle-induced background spectra of the Chandra ACIS-I and the S1, S2, and S3 CCDs, and developed a tool to generate a spectral model for an arbitrary celestial observation.