A muon beam polarimeter was built for the SMC experiment at the CERN SPS, for beam energies of 100 and 190 GeV. The beam polarisation is determined from the asymmetry in the elastic scattering off the polarised electrons of a ferromagnetic target whose magnetisation is periodically reversed. At muon energies of 100 and 190 GeV the measured polarisation is P-mu = -0.80 +/- 0.03 (stat.) +/- 0.02 (syst.) and P-mu = - 0.797 +/- 0.011 (stat.) +/- 0.012 (syst.), respectively. These results agree with measurements of the beam polarisation using a shape analysis of the decay positron energy spectrum. (C) 2000 Elsevier Science B.V. All rights reserved.