Infection of human cells by the SARS-CoV2 relies on its binding to a specific receptor and subsequent fusion of the viral and host cell membranes. The fusion peptide (FP), a short peptide segment in the spike protein, plays a central role in the initial penetration of the virus into the host cell membrane, followed by the fusion of the two membranes. Here, we use an array of molecular dynamics (MD) simulations taking advantage of the Highly Mobile Membrane Mimetic (HMMM) model, to investigate the interaction of the SARS-CoV2 FP with a lipid bilayer representing mammalian cellular membranes at an atomic level, and to characterize the membrane-bound form of the peptide. Six independent systems were generated by changing the initial positioning and orientation of the FP with respect to the membrane, and each system was simulated in five independent replicas, each for 300 ns. In 73% of the simulations, the FP reaches a stable, membrane-bound configuration where the peptide deeply penetrated into the membrane. Clustering of the results reveals three major membrane binding modes (binding modes 1-3) where binding mode 1 populates over half of the data points. Taking into account the sequence conservation among the viral FPs and the results of mutagenesis studies establishing the role of specific residues in the helical portion of the FP in membrane association, the significant depth of penetration of the whole peptide, and the dense population of the respective cluster, we propose that the most deeply inserted membrane-bound form (binding mode 1) represents more closely the biologically relevant form. Analysis of FP-lipid interactions shows the involvement of specific residues, previously described as the “fusion active core residues”, in membrane binding. Taken together, the results shed light on a key step involved in SARS-CoV2 infection with potential implications in designing novel inhibitors.