Modality is "a means used by a speaker to express his opinion or attitude towards the proposition that the sentence expresses or the situation that the proposition describes" (Lyons 1977:452). It has long been an essential semantic category of language in speaking and writing. In traditional grammar, grammarians equate modality with modal expressions used on syntax or morphemes and in syntactic and semantic analysis, so it is chiefly used to refer to the way in which the meaning of a sentence or clause may be modified through the use of a modal auxiliary. As the most frequently used modal auxiliary verbs in English, both can and may show ambiguity among the three-dimensional meaning items "ability", "possibility" and "permission" though there are important syntactic relations between the two modals and these relations differ according to the kind of modality involved. This thesis tries to give ELT some hints as to how to learn synonymous words or senses by exploring three-dimensional senses of can and may as well as interrelations among the three senses "ability", "possibility" and "permission".The first chapter explores the development and taxonomies of modality, with an eye to explaining how a cluster of related meanings-epistemic, deontic, dynamic, and other-is expressed by the same set of lexical items. Chapter two provides a general idea of modal auxiliaries from aspects of grammar, logic, semantics and cognition aspects. Here we would find that, as a main way of modality, modal verbs are a complex phenomenon. Chapter three proposes the theoretical basis of this paper by identifying different empirical and theoretical researches on modality. Chapter four involves senses "ability", "permission", "possibility" and syntactic features of can and may. As the core, chapter five tries to find some common grounds between can and may by sketching a transverse comparison between them. The results indicate that even in some cases when can and may are interchangeable grammatically, they show slight pragmatic differences. Then assumed interrelations among the three-dimensional senses are also derived. It seems that "possibility" is the core and the other two go around it, since both "permission"(viz. deontic possibility) and "ability"(viz. a kind of dynamic possibility) can be interpreted as related with "possibility". Some valuable implications for language learners and teachers are also provided in the last but one chapter. It will exemplify EFL learners’ misuses of can and may and suggest ways of rectifying the errors by adopting the method proposed in this paper. The final chapter offers some conclusions of this study, as well assuggestions for further research.The present paper compares synonymous modals can and may as well as exploring interpretations of common meanings they share, instead of articulating a new theory of modal semantics, so it is primarily a methodological one. Our emphasis is not on naming, labeling, and coding (new) meanings; rather it is on understanding the varied meanings as well as their interactions to which the use of the modals contribute and on describing the processes of our understanding. It also attempts to show that the modals’ behavior constitutes defining characteristic of the modals themselves, a characteristic that should be taught and learned. Extendedly this research expects to suggest that the comparative features of can and may are not specialized in English, other languages also have such features. This is expected to mark an important step forward in ELT. Language teachers should apply this universal feature by comparing similar senses that different modal verbs, even other words or phrases would display in different contexts. Likewise, EFL learners are expected to benefit from it.