Abundances of 15 chemical elements have been derived for 28 F and 16 A stars members of the Hyades open cluster in order to set constraints on self-consistent evolutionary models including radiative and turbulent diffusion. A spectral synthesis iterative procedure was applied to derive the abundances from selected high quality lines in high resolution high signal-to-noise spectra obtained with SOPHIE and AURELIE at the Observatoire de Haute Provence. The abundance patterns found for A and F stars in the Hyades resemble those observed in Coma Berenices and Pleiades clusters. In graphs representing the abundances versus the effective temperature, A stars often display abundances much more scattered around their mean values than the coolest F stars do. Large star-to-star variations are detected in the Hyades A dwarfs in their abundances of C, Na, Sc, Fe, Ni, Sr, Y and Zr, which we interpret as evidence of transport processes competing with radiative diffusion. In A and Am stars, the abundances of Cr, Ni, Sr, Y and Zr are found to be correlated with that of iron as in the Pleiades and in Coma Berenices. The ratios [C/Fe] and [O/Fe] are found to be anticorrelated with [Fe/H] as in Coma Berenices. All Am stars in the Hyades are deficient in C and O and overabundant in elements heavier than Fe but not all are deficient in calcium and/or scandium. The F stars have solar abundances for almost all elements except for Si. The overall shape of the abundance pattern of the slow rotator HD30210 cannot be entirely reproduced by models including radiative diffusion and different amounts of turbulent diffusion. While part of the discrepancies between derived and predicted abundances could be due to non-LTE effects, the inclusion of competing processes such as rotational mixing and/or mass loss seems necessary in order to improve the agreement between the observed and predicted abundance patterns.