  Let $\mathfrak{g}$ be a classial Lie algebra and $\mathfrak{p}$ be a maximal
parabolic subalgebra. Let $M$ be a generalized Verma module induced from a one
dimensional representation of $\mathfrak{p}$. Such $M$ is called a scalar type
generalized Verma module. Its simple quotient $L$ is a highest weight moudle.
In this paper, we will determine the reducibility of such scalar type
generalized Verma modules by computing the Gelfand-Kirillov dimension of $L$.
