The response of a Silicon Photomultiplier (SiPM) to optical signals is affected by many factors including optical cross talk, afterpulsing, dark current, detector dead time, recovery time and gain. Many of these parameters vary with over-voltage. When used to detect scintillation light, it is difficult to relate the response of the SiPM with the incident light and the relationship can be highly nonlinear. In this paper, we propose a Monte Carlo (MC) model for simulating the response of the SiPM to scintillation induced light pulses, which can be used to relate the optical signal with the SiPM response. Developing further on the previous works in this field, the model simulates the various aspects of SiPM response, including photon detection efficiency, recovery time, gain variation and dead time while accounting for the temporal and statistical distribution of the incident light, optical cross-talk, afterpulsing and dark current. It also considers the variation of the different SiPM parameters with varying over-voltage. We have also derived analytic expressions for the single photon response and the voltage drop across the quenching resistance, that help in accurate simulation of the SiPM response. The model compares well with the measurements on a SiPM based scintillation detector. It is also in agreement with the expected mathematical response when the input is an instantaneous light pulse.