The rational treatment of uncertainties in Computational Mechanics has received increasing attention inasmuch critical decisions are supposed to be taken based on computational simulation. Loading conditions, material properties, geometry and shape domain show, in some cases, considerable variability. Moreover, computational models require detailed description of variables and parameters that are, often, not available. Observations and measurements of physical processes as well as parameters clearly show their random characteristics. Statistical and probabilistic procedures provide a sound framework and a rational basis for addressing these uncertainties. In addition to parameter uncertainties, model uncertainties also play a focal role in modern computational mechanics. In reality, neither the true model nor the model parameters are deterministically known. A consequence of model uncertainties and random model parameters is the possibility of undesirable performance of engineering systems. A rational, quantitative treatment of uncertainties allows determination of the probabilities, and associated risks, of undesirable system performance. Hence, rational treatment of uncertainties is fundamental for proper decision making in presence of risk. The main goal of this mini-symposium is to bring together recent research efforts towards building robust and reliable numerical models, through a rational addressing of uncertainties.