Silicon photomultipliers (SiPM) have become increasingly popular in radiation detection design due to smaller profiles, lower operating voltage, and magnetic insensitivity. However, there are nonlinear effects that make modeling SiPM challenging. This study looks at using a Monte Carlo approach to modeling the output of an SiPM and front end electronics for a slow scintillation pulse (CsI(Tl)) and then verifying the results with measurements. The SiPM circuit and front-end electronics were designed in LT Spice for the simulation. In order to define the current source within the SiPM model, a python script was written using a Monte Carlo approach simulating microcells firing throughout the scintillation process. Measurements were taken from a physical circuit and compared. It was found that the rising edge agreed well with measurements. However, the falling edge showed an over-estimate on the SiPM output and an underestimate on the amplifier output. The SiPM output amplitude was likely due to a difference in the simulated light yield and actual light yield from the scintillation crystal. The difference in the falling edge was likely due to errors in the modeling of the CsI(Tl) scintillation decay. Overall this model produced a good estimate for the output from front end electronics.