In this paper as a generalization of skeletons of monomial idelas, we define the skeletons of $\ZZ^n$ graded $S$ modules and study some of its basic properties. It is shown that if $M$ is a finitely generated $\ZZ^n$-graded $S=K[x_1,...,x_n]$-module, then depth of $M$ is qual to the maximum skeletons of $M$ which is Cohen-Macaulay
