Like English, Korean employs several complicated types of cleft constructions. This paper deals with two main types of Korean cleft constructions: predicational and identificational. It first reviews the formal properties of these two types and then provides a constraint-based analysis that can be computationally implemented. In particular, the paper assumes two types of noun KES (one as a common noun and the other as a bound noun) and treats the argument-gapped cleft clause similar to relative clauses while treating the adjunct-gapped cleft clause as a noun-complement construction. The paper further shows that the cleft constructions are closely linked to the copula constructions, sharing many common properties while having their own constructional constraints.