Abstract: In this paper, some necessary and suffcient conditions that a finite lattice impli-cation algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if (L,≤) is a chain, if and only if there exists the unique dual atom in L. Also, it is given that a finite lattice implication algebra with order of a prime number is simple.

Key words: lattice implication algebra, simplicity, periodicity