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Infection of human cells by the SARS-CoV2 relies on its binding to a specific receptor and subsequent fusion of the viral and the 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 extensive 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 human cellular membranes at an atomic level, and to characterize its membrane-bound form. Six independent systems were generated by changing the initial positioning and orientation of the FP with regard to the membrane, and each system was simulated in five independent replicas. In 60% of the simulations, FPs reached a stably membranebound configuration where the peptide deeply penetrated into the membrane. Clustering of the results reveals two major membrane binding modes, the helix-binding mode and the loop-binding mode. Taken into account 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, we propose that the helix-binding mode is the biologically relevant form. In this binding mode, the helix is stabilized in an oblique angle with respect to the membrane with the N-terminus tilted towards the membrane core. Analysis of the FP-lipid interactions shows the involvement of the fusion active core residues of the helix in membrane binding. These results shed light on a key step involved in the process of viral infection by SARS-CoV2 with potential use in designing novel inhibitors.