<p>Cloud model (CM) theory combines random system theory and fuzzy set theory to realize the mutual transformation between qualitative numerical features and quantitative data, providing a method for modeling and quantifying uncertainty problems. Based on the cloud model theory, this paper proposes a multidimensional generalized normal cloud model (MGNCM) for uncertainty propagation. First, the correlation coefficient between the different dimensions is introduced into the multidimensional normal cloud model by using the linear transformation relation, and the multidimensional forward cloud transformation (MFCT) method for generating the multidimensional cloud drops is constructed by the invariant of moments. Meanwhile, the multidimensional backward cloud transformation (MBCT) method for estimating the numerical features of the samples is constructed based on the backward cloud transformation (BCT) algorithm and the moment estimation method. A multidimensional linear cloud transformation (MLCT) method has been proposed for the propagation of uncertainty, with the main applicability in the field of linear transformations. The MGNCM is shown to be applicable to the field of multidimensional uncertainty modeling, quantification and propagation. The value of MGNCM and related algorithms in the field of multidimensional uncertainty modeling and propagation can be demonstrated through a series of numerical examples.</p>