Relatively short peptides, such as toxins and antimicrobial-peptides, are known to insert themselves into cell membranes. On the basis of simple bead-spring models for the membrane lipids, the peptide, and water, detailed processes of the peptide insertion is investigated by molecular dynamics simulation; our special concern is in the highly cooperative motions of membrane lipids and the peptide. Our model lipid has a head group of three hydrophilic beads and a tail of seven hydrophobic beads, while the model peptide is a block-copolymer made of hydrophilic and hydrophobic blocks, with total length of 200 beads. In addition, each water molecule is represented by a single bead which has considerably larger interaction energy. We first confirm that our present lipid model can support spontaneous formation of bilayers in water. Then we place the model peptide near the bilayers and monitor the microscopic process of the adsorption, insertion, and translocation of the peptide. When the peptide molecule is set free to interact with the membrane, the hydrophobic blocks of the peptide strongly favor intimate contact with the lipid tails. This strong attractive interaction gives rise to a severe membrane perturbation, which leads to the formation of a pore, though short-lived, in the membrane. It is found that the side-surface of the pore is almost covered with the hydrophilic heads of the lipids, which seems to help the hydrophilic blocks of the peptide translocate across the membrane. We also monitor the rate of flip-flop inversion of the directions of lipids, and we find it markedly increases during the peptide contact and insertion. The peptide insertion/translocation, the formation of membrane pore, and the flip-flop motions of the lipids are thus found to be closely interconnected.