We present new observations of the lensing cluster SMACSJ2031.8-4036 obtained with the MUSE integral field spectrograph as part of its commissioning on the Very Large Telescope. By providing medium-resolution spectroscopy over the full 4750-9350 Angstroms domain and a 1x1 arcmin2 field of view, MUSE is ideally suited for identifying lensed galaxies in the cluster core, in particular multiple-imaged systems. We perform a redshift analysis of all sources in the datacube and identify a total of 12 systems ranging from $z=1.46$ to $z=6.4$, with all images of each system confirmed by a spectroscopic redshift. This allows us to accurately constrain the cluster mass profile in this region. We foresee that future MUSE observations of cluster cores should help us discover very faint Lyman-alpha emitters thanks to the strong magnification and the high sensitivity of this instrument.