In ring theory it is well known that a ringRwith identity is isomorphic to a matrix ring if and only ifRhas a set of matrix units. In this paper, the above result is extended to matrix near-rings and it is proved that a near-ringRwith identity is isomorphic to a matrix near-ring if and only ifRhas a set of matrix units and satisfies two other conditions. As a consequence of this result several examples of matrix near-rings are given and for a finite group (Γ, +) witho(Γ)> 2 it is proved thatM0(Γn)is (isomorphic to) a matrix near-ring.