This paper is devoted to maximal antichain lattices of posets of arbitrary length. Maximal antichain lattices of finite posets of length 1 have been well studied and are applied, for example, in formal concept analysis. However, there are many general properties inherent in finite posets of any length. For an arbitrary element x of some poset, we introduce the notions of smallest and largest maximal antichains containing x, which are denoted by m(x) and M-x , respectively. We prove that the equality A = boolean OR (x is an element of A) m(x) = boolean AND(x is an element of A) M-x holds for any maximal antichain A. This equality allows us to describe all irreducible elements of maximal antichain lattices. The main result of this paper is a description of all finite posets whose maximal antichain lattice is isomorphic to a given lattice. Irreducible elements play a key role in this description.