It is the first time to do investigation the reliability and validity of thirty kinetic and isotherm models for describing the behaviors of adsorption of silver nanoparticles (AgNPs) onto different adsorbents. The purpose of this study is therefore to assess the most reliable models for the adsorption of AgNPs onto feasibility of an adsorbent. The fifteen kinetic models and fifteen isotherm models were used to test secondary data of AgNPs adsorption collected from the various data sources. The rankings of arithmetic mean were estimated based on the six statistical analysis methods of using a dedicated software of the MATLAB Optimization Toolbox with a least square curve fitting function. The use of fractal-like mixed 1, 2-order model for describing the adsorption kinetics and that of Fritz-Schlunder and Baudu models for describing the adsorption isotherms can be recommended as the most reliable models for AgNPs adsorption onto the natural and synthetic adsorbent materials. The application of thirty models have been identified for the adsorption of AgNPs to clarify the usefulness of both groups of the kinetic and isotherm equations in the rank order of the levels of accuracy, and this significantly contributes to understandability and usability of the proper models and makes to knowledge beyond the existing literatures.