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Consideration of uncertainties in bridge structural engineering is a growing topic because it provides valuable information on the reliability of bridges in time while addressing life-cycle aspects. Utilization of nonlinear finite element method (NLFEM) and Monte Carlo (MC) type simulation is essential for modelling of the concrete bridge random behaviour and its reliability assessments. Generally, a physical problem can be represented by a mathematical model, which depends on input parameters (material characteristics, geometry, etc.). The aim of the stochastic analysis is to propagate uncertainties through a mathematical model to gain statistical information from the output as well as information about the sensitivity of the mathematical model to uncertainties in input variables. However, in bridge engineering, the mathematical model can be quite complex and uncertainty propagation solved by classical MC approach is very difficult to perform as MC type simulation involves large number of numerical evaluations of structural response. Therefore, advanced statistical and reliability techniques, including meta-modelling, have to be applied. The paper describes methodology of such integrated approach for a routine complex assessment utilizing developed software tools and practical application of the approach for selected case studies of concrete bridges from Czech Republic. [ABSTRACT FROM AUTHOR]