MoEDAL (the Monopole and Exotics Detector at the LHC) searches directly magnetic monopoles at the Interaction Point 8 of the Large Hadron Collider (LHC). As an upgrade of the experiment an addition, MAPP (MoEDAL Apparatus for Penetrating Particles) detector extends the physics reach by providing sensitivity to milli-charged and long-lived exotic particles. The MAPP detectors are scintillator detectors, and they are planned, or already installed in service tunnels of the LHC, locating from 50 to 100 meters from the IP8 .
To study and to support the data analysis of the detectors, a complete simulation model of the detector regions was developed. This Geant4  based model consists of all tunnel and accelerator components between the detectors and the IP8, and the material budget, about 100 meters thick ground layer above the tunnels for cosmic background studies. In addition, new physics models describing the interactions of exotic particles, such as millicharged particles, has been implemented in the model.
The geometry description of the model utilises CAD to GDML conversion and parser of Geant4. This allowed to construct modular elements which can be changed without the need of recompiling the software code. In addition, the physics processes are handled in stacks which allows to limit the required computing resources. Various physics generators, such as Pythia8 , are used as a primary input.
In this contribution I will discuss about the development of the geometry models and present the new physics models and interactions that are used in the simulations. I will also show some examples of the detector response for various types of physics models.
 B. Acharya et al, MoEDAL-MAPP, an LHC Dedicated Detector Search Facility, in Proceedings of 2022 Snowmass Summer Study (2022) arXiv:2209.03988 [hep-ph].
 J. Allison et al., Recent developments in Geant4, Nucl. Instr. Meth. A 835 (2016) p. 186-225.
 T. Sjostrand, The Pythia event generator: Past, present and future, Comput. Phys. Comm. 246 (2020) 106910 arXiv:1907.09874v1 [hep-ph].
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