The dynamic analysis of municipal solid waste (MSW) is essential for optimizing landfills and advancing sustainable development goals. Assessing damping ratio (D), a critical dynamic parameter, under laboratory conditions is costly and time-consuming, requiring specialized equipment and expertise. To streamline this process, this research leveraged several novel ensemble machine learning models integrated with the equilibrium optimizer algorithm (EOA) for the predictive analysis of damping characteristics. Data were gathered from 153 cyclic triaxial experiments on MSW, which examined the age, shear strain, weight, frequency, and percentage of plastic content. Analysis of a correlation heatmap indicated a significant dependence of D on shear strain within the collected MSW data. Subsequently, five advanced machine learning methods—adaptive boosting (AdaBoost), gradient boosting regression tree (GBRT), extreme gradient boosting (XGBoost), random forest (RF), and cubist regression—were employed to model D in landfill structures. Among these, the GBRT-EOA model demonstrated superior performance, with a coefficient of determination (R2) of 0.898, root mean square error of 1.659, mean absolute error of 1.194, mean absolute percentage error of 0.095, and an a20-index of 0.891 for the test data. A Shapley additive explanation analysis was conducted to validate these models further, revealing the relative contributions of each studied variable to the predicted D-MSW. This holistic approach not only enhances the understanding of MSW dynamics but also aids in the efficient design and management of landfill systems.