To improve the computational efficiency of nonlinear dynamic probabilistic analysis for aeroengine typical components, an extremum response surface method based on the support vector machine (SVM ERSM) was proposed in this paper. The basic principle was introduced and the mathematical model was established for the SVM ERSM. The probabilistic analysis of turbine casing radial deformation was taken as an example to validate the SVM ERSM considering the influences of nonlinear material property and dynamic heat loads. The results of probabilistic analysis imply that the distribution features of random parameters and the major factors are gained for more accurate the design of casing radial deformation. The SVM ERSM offers a feasible and valid method, which possesses high efficiency and high precision in the nonlinear dynamic probabilistic analysis. Moreover, the SVM ERSM is promising to provide an useful insight for casing dynamic optimal design and the blade-tip clearance control of aeroengine high pressure turbine.