The basic problem of fundamental astrometry is to relate the instrumental reference frame of an observer to the frame defined by ephemerides of stars and objects in the Solar System. It is shown that in principle the choice of definition of the Ephemeris Reference Frame (ERF) can be quite arbitrary. For convenience, it is argued that the ERF should be defined by the rotation of an axi-symmetric rigid model Earth, the celestial pole being the direction of the axis of figure. This definition has practical and theoretical advantages over a model-dependent definition which attempts to take account of non-rigidity of the actual Earth.