  The representations of the quantum toroidal algebras have been widely studied
by many authors. However, no one has constructed some finite dimensional
modules for them while $q$ is generic. In this paper, for all
$\mathfrak{g}$-generic $q$, if $\mathfrak{g}$ is not of type $A_1$, we prove
that the quantum toroidal algebra $U_q(\mathfrak{g}_{\rm tor})$ has no
nontrivial finite dimensional simple module.
