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ISO/ASME geometrical tolerancing standards point out the significance of applying material conditions, which not only is convenient for manufacturing but also does not disturb the free assembly of parts. Unfortunately, the influence of material conditions is rarely considered in the existing studies on statistical geometrical tolerance analysis. Ignoring the influence of material conditions related to the dimensional and geometrical tolerances will directly lead to reduce the accuracy of tolerance analysis. In this paper, a new statistical tolerance analysis approach for mechanical assemblies with dimensional and geometrical tolerances under material conditions is proposed. The proposed approach is fully compatible with the ISO/ASME geometrical tolerancing standards and takes into account the application of various material conditions such as envelope requirement (ER), maximum material condition (MMC), least material condition (LMC), and reciprocity requirement (RPR). The tolerance zones of dimensional and geometrical feature variations are modeled based on the concept of small displacement torsor (SDT), in which torsor models that describe assembly variations caused by complex parallel joints between mating parts are mainly studied. Then, the material conditions effects for features of size with pin/hole and tab/slot shapes are modeled as additional constraints of torsor parameters. After integrating these torsor parameters into the unified Jacobian–Torsor model, a new approach of statistical geometrical tolerance analysis containing the application of material conditions is presented based on the combination of the unified Jacobian–Torsor model and Monte Carlo simulation. Finally, the centring pin assembly is taken as an example to illustrate the application of the proposed approach. [ABSTRACT FROM AUTHOR]