The causes of cerebral lateralization of cognitive and other functions are currently not well understood. To investigate one aspect of function lateralization, a bihemispheric neural network model for a simple visual identification task was developed that has two parallel interacting paths of information processing. The model is based on commonly accepted concepts concerning neural connectivity, activity dynamics, and synaptic plasticity. A combination of both unsupervised (Hebbian) and supervised (Widrow-Hoff) learning rules is used to train the model to identify a small set of letters presented as input stimuli in the left visual hemifield, in the central position, and in the right visual hemifield. Each visual hemifield projects onto the contralateral hemisphere, and the two hemispheres interact via a simulated corpus callosum. The contribution of each individual hemisphere to the process of input stimuli identification was studied for a variety of underlying asymmetries. The results indicate that multiple asymmetries may cause lateralization. Lateralization occurred toward the side having larger size, higher excitability, or higher learning rate parameters. It appeared more intensively with strong inhibitory callosal connections, supporting the hypothesis that the corpus callosum plays a functionally inhibitory role. The model demonstrates clearly the dependence of lateralization on different hemisphere parameters and suggests that computational models can be useful in better understanding the mechanisms underlying emergence of lateralization.