Abstract: Uncertainties in environmental loads and structural parameters are challenging phenomena which influence the structural design, the assessment and prediction of structural performance, and the damage identification of structures in service. These uncertainties may variously be objective or subjective from different sources, requiring appropriate mathematical modeling and quantification to obtain realistic analysis results of the behavior and reliability of engineering structures. In general, these uncertainties in different types and from multiple sources need to be described by different quantification models, involving probabilistic model, imprecise probabilistic model and non-probabilistic model. In addition, uncertainties may be time-varying during service time, and the direct measurements of uncertain variables are sometimes difficult to be carried out during the service of the structure. However, the performance test data, such as displacements, and stresses of structures, may be much more easily obtained when compared with the direct measurements. Facing the above issues, a novel uncertainty quantification model named P-CS (probability-convex set) model is proposed in this paper to enable uncertainties from multiple sources quantified in a uniform model. The P-CS model characterizes uncertainties as a combination of probabilistic random variables and a non-probabilistic convex set based on the principle of probability equivalence, which can make probabilistic model, imprecise probabilistic model and non-probabilistic model expressed under a uniform framework. On the basis of the P-CS model, a Bayesian updating method is proposed in this paper driven by performance test data. In this updating method, the allowable ranges of the parameters of P-CS model are divided into several subintervals respectively and then the credibility distribution of each parameter can be updated according to the performance test data, finally, parameters of P-CS model can be updated based on the posterior credibility distributions. Three numerical examples show the construction methods and the probabilistic and non-probabilistic properties of the P-CS model, and two mechanical examples are presented to validate the proposed Bayesian updating method.