Understanding how nanoparticles with different shapes interact with cell membranes is important in drug and gene delivery, but this interaction remains poorly studied. Using computer simulations, we investigate the physical translocation processes of nanoparticles with different shapes (for example, spheres, ellipsoids, rods, discs and pushpin-like particles) and volumes across a lipid bilayer. We find that the shape anisotropy and initial orientation of the particle are crucial to the nature of the interaction between the particle and lipid bilayer. The penetrating capability of a nanoparticle across a lipid bilayer is determined by the contact area between the particle and lipid bilayer, and the local curvature of the particle at the contact point. Particle volume affects translocation indirectly, and particle rotation can complicate the penetration process. Our results provide a practical guide to geometry considerations when designing nanoscale cargo carriers.