Focusing on the quantification of mixed-uncertainty in nonlinear mechanical systems, a confidence region method for the quantification of aleatory and epistemic uncertainty is presented. In this method, interval analysis is used to represent epistemic uncertainty while probability theory is used to represent aleatory uncertainty, in order to obtain the confidence region of mixed uncertainties. Then, the traditional double-loop Monte Carlo sampling approach is improved to propagate uncertainties during the entire time domain. Finally, a nonlinear mass-spring-damper system is simulated to discuss the validity of the analysis method based on mixed-uncertainty. The results show that it can improve the reliability of the system’s design when both aleatory and epistemic uncertainties of the parameters are considered, and can set a theoretical foundation for the dynamic design and precision analysis of nonlinear mechanical systems.