Structural uncertainty is commonly encountered in practical structural engineering problems. Considering the impact of uncertain factors on modal parameters is of significant importance in enhancing the robustness of structural dynamic analysis. In most developed methods involving the solution or estimation of random modal parameters for linear structures, the modal parameters are usually seen as Gaussian variables, and correlation among them is not getting much attention. However, the Gaussian and independence assumptions of the random mode parameters create simulation errors, affecting the robustness of the structural dynamics response predictions. To address this issue, this study proposed two approaches for simulating random modal parameters of respective discrete and continuous structures. For a discrete structure, its mode shapes are discrete. The random modal parameters are treated as correlated random variables. The correlated polynomial chaos expansion (c-PCE) method was applied to simulate non-Gaussianity and correlation based on the statistics of modal parameters. For continuous structures, random mode shapes are seen as correlated random fields. They can be represented in terms of correlated random variables by using the improved orthogonal series expansion method. Then they were combined with random natural frequencies to constitute a set of correlation variables, which are enabled to be simulated using standard Gaussian variables by utilizing the c-PCE. Finally, taking the truss structure and the plate structure respectively as examples, considering the non-Gaussianism of the modal parameters caused by the fluctuation of material parameters, the proposed random mode parameters can accurately simulate the statistical characteristics of the modal parameters, and further predict the random response of the structure. The simulation results verify the simulation accuracy of the proposed method for the random mode parameters and the necessity to consider the parameter correlations.