Compared with the probability approach, the non-probabilistic convex model only requires a small amount of samples to obtain bounds of the imprecise parameters, and whereby makes the uncertainty analysis more convenient and economical.At the present time, there are two principal non-probabilistic convex models: Interval Model and Ellipsoid Model.Theoretically Interval Model can only deal with the problems in which the imprecise parameters are independent, while Ellipsoid Model can only deal with the problems in which the imprecise parameters are dependent.However, in many practical engineering problems uncertainties are often from multiple sources associated with the material properties loads, geometrical dimensions, boundary conditions, etc.That is to say, some uncertain parameters have dependence while some ones are independent to each other.If we use the Interval Model or Ellipsoid Model to deal with such a problem, some serious difficulties will be encountered.In this paper, we attempt to propose a new type of non-probabilistic convex model for uncertainty quantification of structures, named as Multidimensional-Parallelepiped Model as shown in Fig.i, which is able to handle the problems with both independent and dependent imprecise parameters.The dependence of two parameters are quantitatively described through a correlation angle defined in the corresponding bivariant parameter space.Based on the correlation angle, a correlation coefficient is also defined for any pair of parameters.Using the marginal intervals of all the parameters and also the correlation coefficients of all pair of the parameters a multidimensional-parallelepiped model can then be created to represent the uncertainty extent of the problem.To make the uncertainty analysis more convenient and efficient, an affine coordinate system is introduced to transform the multidimensional-parallelepiped uncertainty domain to a regular multidimensional box.The suggested new convex model is applied to the structural uncertainty propagation analysis, and corresponding structural response bounds are computed for both static and dynamic problems.Several numerical examples are investigated to demonstrate the effectiveness of the present method.