We report the numerical scheme that was developed within the framework of classical molecular dynamics methods for atomistic simulation of the deposition of Ag atoms onto the surface of two-dimensional (2D) titanium carbide Ti2C (MXene) and the growth of silver nanoparticles (NP). Developed model adopts hybrid interatomic potential, where interactions between metal atoms and between metal-carbon are described within different methods. Proposed model can be used to study similar systems consisting of other metals, as well as two-dimensional carbides Ti(n + 1)Cn with n  2 and 3. Experiments on simulation of the deposition of silver atoms onto the surface of two-dimensional titanium carbide Ti2C with three different values of the growth surface area were performed. To investigate the peculiarities of nanoparticle formation and growth processes, two types of interaction between Ti2C and Ag atoms with the metallic-type bonding and Van der Waals forces were considered. Considered cases simulate deposition onto hydrophilic and hydrophobic surfaces, respectively. It is shown that in case of hydrophilic-type of interaction Ag thin film growth on the substrate, while in case of hydrophobic surface, separate nanoparticles are formed. A modeled sample of the system with a silver nanoparticle formed on the surface of two-dimensional titanium carbide was obtained, and forces of interaction between the Ti2C surface and NPs were calculated. In addition to the stationary case, the MXene-NP interaction was also considered under external loading. The friction forces between the nanoparticle and Ti2C were calculated at three different magnitudes of the external load. It is shown that translational movement of the nanoparticle on the MXene surface observed in the case with largest magnitude of external load.