Aims. The hydrogen Lyman lines provide important diagnostic information about the dynamics of the chromosphere, but there have been few systematic studies of their variability during flares. We investigate Doppler shifts in these lines in several flares, and use these to calculate plasma speeds. Methods. We use spectral data from the Multiple EUV Grating Spectrograph B (MEGS-B) detector of the Extreme-Ultraviolet Variability Experiment (EVE) instrument on the Solar Dynamics Observatory. MEGS-B obtains full-disk spectra of the Sun at a resolution of 0.1 nm in the range 37-105 nm, which we analyse using three independent methods. The first method performs Gaussian fits to the lines, and compares the quiet-Sun centroids with the flaring ones to obtain the Doppler shifts. The second method uses crosscorrelation to detect wavelength shifts between the quiet-Sun and flaring line profiles. The final method calculates the "center-of-mass" of the line profile, and compares the quiet-Sun and flaring centroids to obtain the shift. Results. In a study of 6 flares we find strong signatures of both upflow and downflow in the Lyman lines, with speeds measured in Sun-as-a-Star data of around 10 km s −1 , and speeds in the flare excess signal of around 30 km s −1 . Conclusions. All events showing upflows in Lyman lines are associated with some kind of eruption or coronal flow in imaging data, which may be responsible for the net blueshifts. Events showing downflows in the Lyman lines may be associated with loop contraction or faint downflows, but it is likely that chromospheric condensation flows are also contributing.