Cell penetration after recognition of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus by the ACE2 receptor and the fusion of its viral envelope membrane with cellular membranes are the early steps of infectivity. A region of the Spike protein of the virus, identified as the “fusion peptide” (FP), is liberated at its N-terminal site by a specific cleavage occurring in concert with the interaction of the receptor-binding domain of the Spike. Studies have shown that penetration is enhanced by the required binding of Ca2+ ions to the FPs of coronaviruses, but the mechanisms of membrane insertion and destabilization remain unclear. We have predicted the preferred positions of Ca2+ binding to the SARS-CoV-2-FP, the role of Ca2+ ions in mediating peptide-membrane interactions, the preferred mode of insertion of the Ca2+-bound SARS-CoV-2-FP, and consequent effects on the lipid bilayer from extensive atomistic molecular dynamics simulations and trajectory analyses. In a systematic sampling of the interactions of the Ca2+-bound peptide models with lipid membranes, SARS-CoV-2-FP penetrated the bilayer and disrupted its organization only in two modes involving different structural domains. In one, the hydrophobic residues F833/I834 from the middle region of the peptide are inserted. In the other, more prevalent mode, the penetration involves residues L822/F823 from the LLF motif, which is conserved in CoV-2-like viruses, and is achieved by the binding of Ca2+ ions to the D830/D839 and E819/D820 residue pairs. FP penetration is shown to modify the molecular organization in specific areas of the bilayer, and the extent of membrane binding of the SARS-CoV-2 FP is significantly reduced in the absence of Ca2+ ions. These findings provide novel mechanistic insights regarding the role of Ca2+ in mediating SARS-CoV-2 fusion and provide a detailed structural platform to aid the ongoing efforts in rational design of compounds to inhibit SARS-CoV-2 cell entry.