The multiplicity of charged particles in the central rapidity region has been measured by the NA57 experiment in Pb-Pb collisions at the CERN SPS at two beam momenta: 158 A GeV/c and 40 A GeV/c. The value of dN_ch/dη at the maximum has been determined and its behaviour as a function of centrality has been studied in the centrality range covered by NA57 (about 50% of the inelastic cross section). The multiplicity increase is compatible with a logarithmic dependence on the centre of mass energy. The results are compared with those from other experiments and with the VENUS and RQMD models.