We consider the problem of a helium atom under the radiation field of the DESY vacuum ultraviolet (VUV) free electron laser (FEL) (Phase I, h congruent to 13 eV). We find by solving numerically the time-dependent Schrodinger equation, that there is a large probability for resonant two-photon excitation from the ground state into a low kinetic energy state just above the first He ionization threshold. From this it is possible to go into another quasi-free state higher up, by resonant absorption of an additional photon. There is no double ionization of He. These results are in general agreement with the He photoelectron and time-of-flight (TOF) spectra recorded on March 2002, in the last week of the DESY VUV FEL Phase I operation. A detailed report on the experiments is given in a companion paper.722