Context. In the current era of large spectroscopic surveys of the Milky Way, reference stars for calibrating astrophysical parameters and chemical abundances are of paramount importance. Aims: We determine elemental abundances of Mg, Si, Ca, Sc, Ti, V, Cr, Mn, Co, and Ni for our predefined set of Gaia FGK benchmark stars. Methods: By analysing high-resolution spectra with a high signal-to-noise ratio taken from several archive datasets, we combined results of eight different methods to determine abundances on a line-by-line basis. We performed a detailed homogeneous analysis of the systematic uncertainties, such as differential versus absolute abundance analysis. We also assessed errors that are due to non-local thermal equilibrium and the stellar parameters in our final abundances. Results: Our results are provided by listing final abundances and the different sources of uncertainties, as well as line-by-line and method-by-method abundances. Conclusions: The atmospheric parameters of the Gaia FGK benchmark stars are already being widely used for calibration of several pipelines that are applied to different surveys. With the added reference abundances of ten elements, this set is very suitable for calibrating the chemical abundances obtained by these pipelines. Based on NARVAL and HARPS data obtained within the Gaia DPAC (Data Processing and Analysis Consortium) and coordinated by the GBOG (Ground-Based Observations for Gaia) working group and on data retrieved from the ESO-ADP database.Tables C.1-C.35 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/582/A81