A three-dimensional structure of a model decapeptide is obtained by performing molecular dynamics simulations of the peptide in explicit water. Interactions between an N-myristoylated form of the folded peptide anchored to dipalmitoylphosphatidylcholine fluid phase lipid membranes are studied at different applied surface tensions by molecular dynamics simulations. The lipid membrane environment influences the conformational space explored by the peptide. The overall secondary structure of the anchored peptide is found to deviate at times from its structure in aqueous solution through reversible conformational transitions. The peptide is, despite the anchor, highly mobile at the membrane surface with the peptide motion along the bilayer normal being integrated into the collective modes of the membrane. Peptide anchoring moderately alters the lateral compressibility of the bilayer by changing the equilibrium area of the membrane. Although membrane anchoring moderately affects the elastic properties of the bilayer, the model peptide studied here exhibits conformational flexibility and our results therefore suggest that peptide acylation is a feasible way to reinforce peptide-membrane interactions whereby, e.g., the lifetime of receptor-ligand interactions can be prolonged.