<p>Parameter inference and uncertainty quantification play a fundamental role in many fields of science when relating models to real-world data, and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly for models with many unknown parameters and also because the highest posterior density region defines a relatively small region of the parameter space. In recent years, there has been a remarkable development of simulation-based inference (SBI) algorithms, and they have now been applied across a wide range of areas. There are a number of key advantages to these methods, centered around the ability to perform statistical inference without an explicit likelihood. The method used in this study is the approximate Bayesian computation (ABC) using an ellipsoidal nested sampling (NS) technique. The ABC constructs a sequence of distributions based on the accepted particles and converges gradually to the exact posterior distributions by decreasing progressively a tolerance threshold measuring the similarity between model predictions and observed data. To enhance the computational efficiency of the sampler, the concept of <i>minimum-volume enclosing ellipsoid</i> (MVEE) is adopted to better delimit the parameter space around the most promising region. The computational efficiency of the proposed sampler is illustrated through different mechanical systems and structures with simulated and real data showing the versatility and the adaptability of the SBI method to deal with parameter inference and uncertainty quantification.</p>