Based on the example of the quadratic polynomial without cross terms outputs, the structural and correlative contributions of the correlated normal input variables were derived out, which had impact on the variance contributions of output response variables. Numerical results of several examples validate the correctness of analytical solutions. Comparing the presented indices with the existent indices, some general conclusions were drawn from the structural contributions and the correlative contributions, and the differences between them were identified. The proposed analytical solutions can be directly used to identify the structural contributions and the correlative contributions of the quadratic polynomial without cross terms, which offer a reference to other numerical algorithms.