This work is a contribution to the study of the elementary excitations and magnetic properties of a super-lattice such as [Co(tm)/Cu(tnm)]N, represented by the N atomic planes Heisenberg ferromagnetic system where the nearest neighbour and next nearest neighbour exchange, and dipolar interactions are considered in addition to the surface anisotropy. This study is based on the linear spin waves theory. In the presence of the exchange alone, the excitation spectrum E(k) and the magnetization < S > analytical expressions are obtained for N=3, 5 and 10 atomic planes using the Green’s function formalism. We also highlighted the existence of N excitation modes in conformity with former studies. A numerical study of the surface anisotropy and dipolar interaction contributions is also reported. A good agreement between the calculated and measured magnetization evolution with an applied magnetic field at 300K is obtained.