Motivated by the theory of 0-simple semigroup and M -semigroup, in this paper we introduce the notion of 0-simple M -semigroup. We also focus our research towards soft set theory and introduce the notion of soft Msemigroup and provide some results on it. In a 0-simple M -semigroup, we prove that 0-minimal ideal is a 0-simple M -semigroup and in soft setting, we prove that the union of the two soft M -semigroups is also a soft M -semigroup with the condition that the intersection of the subsets

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... re empty. Also we justify that the Cartesian product of the two soft M -semigroups is also a soft M -semigroup.