We aim at studying the effect of radial motions on the spectrum emitted by moving prominences in the helium resonance lines and at facilitating the interpretation of observations, in order to improve our understanding of these dynamic structures. We develop our non-local thermodynamic equilibrium radiative transfer code formerly used for the study of quiescent prominences. The new numerical code is now able to solve the statistical equilibrium and radiative transfer equations in the non-static case by using velocity-dependent boundary conditions for the solution of the radiative transfer problem. This first study investigates the effects of different physical conditions (temperature, pressure, geometrical thickness) on the emergent helium radiation. The motion of the prominence plasma induces a Doppler dimming effect on the resonance lines of He I and He II. The velocity effects are particularly important for the He II 304 A line as it is mostly formed by resonant diffusion of incident radiation under prominence conditions. The He I resonance lines at 584 and 537 A also show some sensitivity to the motion of the plasma, all the more when thermal emission is not too important in these lines. We also show that it is necessary to consider partial redistribution in frequency for the scattering of the incident radiation. This set of helium lines offers strong diagnostic possibilities that can be exploited with the SOHO spectrometers and with the EIS spectrometer on board the Hinode satellite. The addition of other helium lines and of lines from other elements (in particular hydrogen) in the diagnostics will further enhance the strength of the method.
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