Safety issues for the use of products containing nanoparticles need to be considered, since these nanoparticles may break through human skin to damage cells. In this paper, applied mathematical techniques are used to model the penetration of a spherical gold nanoparticle into an assumed circular hole in a lipid bilayer. The 6–12 Lennard-Jones potential is employed, and the total molecular interaction energy is obtained using the continuous approximation. Nanoparticles of three different radii, namely, 10, 15 and 20 Å, are studied, which are initiated at rest, confined to the axis of the hole. A similar behaviour for these three cases is observed. The critical hole radii at which these nanoparticles enter the bilayer are 12.65, 17.62 and 22.60 Å, respectively. Further, once the hole radii become larger than 20.79, 23.14 and 27.02 Å, respectively, the gold nanoparticles tend to remain at the mid-plane of the bilayer, and do not pass through the bilayer.