In this book, the authors present in detail several recent methodologies and algorithms that they developed during the last fifteen years. The deterministic methods account for uncertainties through empirical safety factors, which implies that the actual uncertainties in materials, geometry and loading are not truly considered. This problem becomes much more complicated when considering biomechanical applications where a number of uncertainties are encountered in the design of prosthesis systems. The reliability and optimization procedures are classically carried out using deterministic constraints, but when considering the living tissues, the constraints become variable, that leads to a different design space at each iteration. There is a strong need to consider this complexity on the material property uncertainty. The mechanical properties change permanently in terms of the mechanical environment, ageing, disease, nutrition and other factors. This book implements improved numerical strategies and algorithms that can be applied to biomechanical studies.