Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr(R(x)) with n=3r or 4r variables, where r＞1 is an odd integer.Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders.Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions.It is demonstrated that our bounds are better than the previously obtained bounds.