This paper is mainly devoted to the embeddings of M-continuous lattices in Hilbert cubes. we establish the subdirect product representation theory of M-continuous lattices,whichgeneralizes and unifies the corresponding work of Raneyt Bruns,Lawson,Bandelt,Erne andothers. The classical technique of Raney and Bruns,baised on the deep investigations of maximalcomplete strict chains of suitable auxiliary relations,is skillful and the situations to which it canapply are limited.comparatively,the method used in this paper not ouly is very natural andconceptual,but also can deal with more general cases.