The problem of accurately accessing the health of structures can be addressed through the use of various numerical and experimental methods. The need to quantify the inconclusiveness accurately is important for an accurate prediction of future response. The basis of model updating is to ensure that models can be found to be a better reflection of the measured information than the initial models. Specifically, structural model updating is the fitting of a current model to reflect better the dynamic response of a structure. An algorithm, based on Gibbs sampling for Bayesian model updating is used to efficiently update the probability density distribution of the parameters. After which the robust failure probability is also updated. The efficacy and effectiveness of this would be illustrated through examples, a 4 degrees of freedom (4-DOF) mechanical system and a ten-story building.