This paper studies the word sense disambiguation of English modal verb ldquomayrdquo. Based on the analysis of the sense, category of modality and function of ldquomayrdquo in different contexts in the training corpus, a model of back propagation neural network for word sense disambiguation of ldquomayrdquo is established. It takes the mutual information of epistemic and non-epistemic ldquomayrdquo and the verb before and after ldquomayrdquo as well as active and passive voice of the sentence as the input vectors. The test to the model shows that the rate for correct disambiguation reaches 78%. This study extends the word sense disambiguation into the level of modality which is a breakthrough in both WSD and linguistic studies.