Lysozyme is an enzyme often used as an antibacterial agent in food industries and biochemical and pharmaceutical laboratories. Immobilisation of lysozyme by encapsulating in a nanotube has received much interest as it can enhance stability of the enzyme in ambient condition. Experimentally, various types of nanotubes have been proposed as a host for lysozyme. Here, we mathematically model the immobilisation process and the interaction between lysozyme and various types of nanotubes in order to compare the effectiveness of different nanotube materials. In this paper, we consider boron nitride, carbon, silicon, silicon carbide and titania nanotubes. For each type of nanotubes, we determine the critical radius that will maximise the interaction between the lysozyme molecule and the nanotube. Our results suggest that titania nanotube stands out as the most promising candidate for lysozyme storage and delivery. The model presented here can be extended to further investigate the interaction between different types of nanotube materials and protein structures for the development of effective molecular storage.