The purpose of this paper is to demonstrate that the occurrence of epenthetic vowels and consonants can be attributed to certain properties of syllable structure and some universal principles of syllabification interacting with (phonotactic) constraints, some of which are universal, others language-specific. The analysis of epenthesis proposed here is an elaboration and refinement of earlier proposals by Singh (1980, 1981a, 1981b, 1981c) and Piggott (1981). We believe that this analysis provides an explanation of the phenomenon of epenthesis. The paper is organized in the following way. In Section 1, we identify the phenomenon of epenthesis and summarize the difficulties in capturing generalizations about it within a framework which treats phonological representations as linear sequences of elements. In Section 2, we outline our conception of syllable structure and examine some of the consequences and implications of our assumptions. Section 3 contains an elaboration of the principles of syllabification that underlie our account of epenthesis. In Section 4, we indicate what we think we have managed to explain and point out some of the significance of the explanation provided. Finally, in Section 5, we try to link our work to some long-held views about the relationship of rules to constraints.