The law of friction has been known since the 18th century but yet, the development on the tribology field was established in the last decades mainly by the invention of frictional force microscope (FFM), which enabled scientist to study friction on atomic levels. To describe the friction phenomena at nanoscale, molecular dynamics (MD) and density functional theory (DFT) models are commonly used, popular models and detailed information about friction can be obtained via those models. On the other hand, reduced-order simplified models such as Prandtl-Tomlinson (PT) model can also provide essential information about friction phenomena and understanding a phenomenon via a simplified model is always motivate. In this thesis, Prandtl-Tomlinson model is generalized into three dimensions and the model is illustrated in both two and three dimensions on various quasi two dimensional crystal structures such as graphene, silicene, germanene and hexagonal boron nitride. By solving the equation of motion of the PT model numerically, friction curves and some parametric dependences of the friction such as anisotropy and friction dependence on external loading force is analyzed. We concluded that the PT model in three dimensions provides good results and can be used to analyze friction phenomena to save from computational cost in MD and DFT models.