Asteroid (234) Barbara is the prototype of a category of asteroids that has been shown to be extremely rich in refractory inclusions, the oldest material ever found in the Solar system. It exhibits several peculiar features, most notably its polarimetric behaviour. In recent years other objects sharing the same property (collectively known as `Barbarians') have been discovered. Interferometric observations in the mid-infrared with the ESO VLTI (Very Large Telescope Interferometer) suggested that (234) Barbara might have a bi-lobated shape or even a large companion satellite. We use a large set of 57 optical light curves acquired between 1979 and 2014, together with the timings of two stellar occultations in 2009, to determine the rotation period, spin-vector coordinates, and 3-D shape of (234) Barbara, using two different shape reconstruction algorithms. By using the light curves combined to the results obtained from stellar occultations, we are able to show that the shape of (234) Barbara exhibits large concave areas. Possible links of the shape to the polarimetric properties and the object evolution are discussed. We also show that VLTI data can be modelled without the presence of a satellite.