Femtosecond laser texturing creates a set of hierarchical micro and nanostructures on solid surfaces allowing a control over their wettability. One of the promising applications of this effect is in the integration and durability of dental and orthopedic implants. It is still unclear, however, why and how the wettability of laser textured surfaces changes with time. The classical models, such as the Wenzel and Cassie-Baxter, have not provided enough explanations and a more realistic study is required. In this work, we used a continuum-level modelling method to study the wetting dynamics of a water droplet on Ti and Ti alloy. The wetting studies were performed on both plain solid surfaces and on surfaces with various reliefs. The calculated evolutions of the contact angle with time for both structured and non-structured surfaces provide explanations of several experimental results. Such simulations are shown to be promising for explaining the wetting mechanism for laser textured materials.