Titanium dioxide nanoparticle (TiO2-NP) is widely used in manufactured nanomaterials such as sunscreens, cosmetics, drugs, and some food products. It can be encapsulated in a single-walled carbon nanotube (SWNT) depending on their physical and chemical interactions. On applying the Lennard-Jones potential function and the continuous approximation, we determine three encapsulation mechanisms for spherical shape TiO2-NP entering a tube: (i) head-on at the tube open end, (ii) around the edge of the tube open end, and (iii) through a defect opening on the tube wall. The total potential energy of the system is obtained as an exact expression by performing double surface integrals. We find that the TiO2-NP is most (least) likely to be encapsulated into a SWNT by head-on configuration (around the edge of the tube open end). This encapsulation procedure is a potential application for targeted drug delivery. For convenience, throughout this analysis all configurations are assumed to be in vacuum and the TiO2-NP is initially at rest.