Structural reliability evaluation is considered to be the solution for modern complex engineering systems possessing uncertain parameters. Reliability estimation involves probabilistic theory when the uncertainties are defined as random variables, whereas with limited resources, it is strenuous to estimate precise parameters in the structural model. Therefore, for such cases, imprecise parameters should be treated appropriately in the design and analysis stage for the improvement of serviceability of the system. On the other side, analyses involving multi-dimensional, computationally expensive, and highly nonlinear structures are formidable in simulation-based methods in the presence of uncertainties. An efficient uncertainty analysis procedure is presented in this paper for analysing the systems with imprecise uncertainties defined as probability-box variables. The estimated bounds of failure probability for the numerical examples from structural mechanics are compared with the traditional approaches to demonstrate the efficiency of the methodology.