The composition of the plasma membrane of malignant cells is thought to influence the cellular uptake of cisplatin and to take part in developing resistance to this widespread anti-cancer drug. In this work we study the permeation of cisplatin through the model membranes of normal and cancer cells using molecular dynamics simulations. A special attention is paid to lipid asymmetry and cholesterol content of the membranes. The loss of lipid asymmetry, which is common for cancer cells, leads to a decrease in their permeability to cisplatin by one order of magnitude in comparison to the membranes of normal cells. The change in the cholesterol molar ratio from 0% to 33% also decreases the permeability of the membrane by approximately one order of magnitude. The permeability of pure DOPC membrane is 5-6 orders of magnitude higher than one of the membranes with realistic lipid composition, which makes it as an inadequate model for the studies of drug permeability.