  In this article we study analytic properties of the multiple Dirichlet series
associated to additive and Dirichlet characters. For the multiple Dirichlet
series associated to additive characters, the meromorphic continuation is
established via obtaining translation formulas satisfied by these multiple
Dirichlet series. While it seems difficult to obtain such a translation formula
for the multiple Dirichlet series associated to Dirichlet characters, we rely
on their intrinsic connection with the multiple Dirichlet series associated to
additive characters in order to investigate their analytic characteristics. We
are also able to determine the exact set of singularities of the multiple
Dirichlet series associated to additive characters.
