By the well-known result of A. H. Clifford, any band of left Archimedean semigroups is a semilattice of matrices (rectangular bands) of left Archimedean semigroups. The converse of this assertion don’t hold, i.e. the class of semilattices of matrices of left Archimedean semigroups is larger than the class of bands of left Archimedean semigroups. In this paper we characterize semilattices of matrices of left Archimedean semigroups, and especially matrices of left Archimedean semigroups. The obtained results generalize the some results of M. S. Putcha and L. N. Shevrin.