We present measurements of elemental abundances in solar flares with the EUV Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO). EVE observes both high temperature Fe emission lines (Fe XV-Fe XXIV) and continuum emission from thermal bremsstrahlung that is proportional to the abundance of H. By comparing the relative intensities of line and continuum emission it is possible to determine the enrichment of the flare plasma relative to the composition of the photosphere. This is the first ionization potential or FIP bias ($f$). Since thermal bremsstrahlung at EUV wavelengths is relatively insensitive to the electron temperature, it is important to account for the distribution of electron temperatures in the emitting plasma. We accomplish this by using the observed spectra to infer the differential emission measure distribution and FIP bias simultaneously. In each of the 21 flares that we analyze we find that the observed composition is close to photospheric. The mean FIP bias in our sample is $f=1.27pm0.23$. This analysis suggests that the bulk of the plasma evaporated during a flare comes from deep in the chromosphere, below the region where elemental fractionation occurs.