  [abridged] We study the evolution of the Star Formation Rate Function (SFRF)
of massive galaxies over the 0.4<z<1.8 redshift range and its implications for
our understanding of the physical processes responsible for galaxy evolution.
We use multiwavelength observations included in the GOODS-MUSIC catalogue,
which provides a suitable coverage of the spectral region from 0.3 to 24 micron
and either spectroscopic or photometric redshifts for each object. Individual
SFRs have been obtained by combining UV and 24 micron observations, when the
latter were available. For all other sources an "SED fitting" SFR estimate has
been considered. We then define a stellar mass limited sample, complete in the
Mstar>1.e10 Msun range and determine the SFRF using the 1/Vmax algorithm. We
define simulated galaxy catalogues based on three different semi-analytical
models of galaxy formation and evolution. We show that the theoretical SFRFs
are well described by a double power law functional form and its redshift
evolution is approximated with high accuracy by a pure evolution of the typical
SFR. We find good agreement between model predictions and the high-SFR end of
the SFRF, when the observational errors on the SFR are taken into account.
However, the observational SFRF is characterised by a double peaked structure,
which is absent in its theoretical counterparts. At z>1.0 the observed SFRF
shows a relevant density evolution, which is not reproduced by SAMs, due to the
well known overprediction of intermediate mass galaxies at z~2. The agreement
at the low-SFR end is poor: all models overpredict the space density of SFR~1
Msun/yr and no model reproduces the double peaked shape of the observational
SFRF. If confirmed by deeper IR observations, this discrepancy will provide a
key constraint on theoretical modelling of star formation and stellar feedback.
