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The present paper focuses on the development of the SimPET simulation tool intended for the estimation of the solidstate photons detector (Silicon Photomultiplier, SiPM, or Multi-Pixel Photon Counter, MPPC) and front-end electronics responses to scintillations generated in LYSO crystals of a PET scanner. The SimPET simulation software is presented, including the description of methods and algorithms used to simulate the photon generation, propagation, impact photon-SiPM, and the behavior of each pixel in the photon detector following this impact. The saturation effects caused by the dead time after each avalanche were taken into consideration, as well as the interdependence between SiPM pixels. The resulting output current vs. time curves obtained by simulation are then presented and compared with the ones obtained experimentally, indicating good agreement. The simulation models of frond-end electronics, including filters, ADCs, and digital signal processing unit are also presented. Finally, the simulation results are discussed in terms of their impact on the energy and position measurement resolution.