Deep 21-cm HI line observations of the Virgo cluster spiral galaxy NGC 4569 have been obtained with the VLA in its D configuration and with the Effelsberg 100-m telescope. A low surface density arm was discovered in the west of the galaxy, whose velocity field is distinct from that of the overall disk rotation. The observed gas distribution, velocity field, and velocity dispersion are compared to snapshots of dynamical simulations that include the effects of ram pressure. Two different scenarios were explored: (i) ongoing stripping and (ii) a major stripping event that took place about 300 Myr ago. It is concluded that only the post-stripping scenario can reproduce the main observed characteristics of NGC 4569. It is not possible to determine if the gas disk of NGC 4569 had already been truncated before it underwent the ram pressure event that lead to its observed HI deficiency.