It is well documented that superior colliculus (SC) neurons integrate stimuli of different modalities (e.g., visual and auditory). In this work, a mathematical model of the integrative response of SC neurons is presented, to gain a deeper insight into the possible mechanisms implicated. The model includes two unimodal areas (auditory and visual, respectively) sending information to a third area (in the SC) responsible for multisensory integration. Each neuron is represented via a sigmoidal relationship and a first-order dynamic. Neurons in the same area interact via lateral synapses. Simulations show that the model can mimic various responses to different combinations of stimuli: i) an increase in the neuron response in presence of multisensory stimulation, ii) the inverse effectiveness principle; iii) the existence of within- and cross-modality suppression between spatially disparate stimuli. The model suggests that non linearities in neural responses and synaptic connections can explain several aspects of multisensory integration.