Understanding and predicting permeability of compounds through skin is of interest for transdermal delivery of drugs and for toxicity predictions of chemicals. We show, using a new atomistic molecular dynamics model of the skin's barrier structure, itself validated against near-native cryo-electron microscopy data from human skin, that skin permeability to the reference compounds benzene, DMSO (dimethyl sulfoxide), ethanol, codeine, naproxen, nicotine, testosterone and water can be predicted. The permeability results were validated against skin permeability data in the literature. We have investigated the relation between skin barrier molecular organization and permeability using atomistic molecular dynamics simulation. Furthermore, it is shown that the calculated mechanism of action differs between the five skin penetration enhancers Azone, DMSO, oleic acid, stearic acid and water. The permeability enhancing effect of a given penetration enhancer depends on the permeating compound and on the concentration of penetration enhancer inside the skin's barrier structure. The presented method may open the door for computer based screening of the permeation of drugs and toxic compounds through skin.