Summary: We introduce the concept of CMS modules. A right \(R\)-module \(M\) is called CMS if every closed \(M\)-cyclic submodule of \(M\) is a direct summand. An example of CMS module which is not CS is given. We characterize semi-simple Artinian rings in terms of CMS modules. We prove that over a right hereditary ring \(R\), every projective right \(R\)-module is a CMS module.