  We define a new equivariant (with respect to a finite group $G$ action)
version of the Poincar\'e series of a multi-index filtration as an element of
the power series ring ${\widetilde{A}}(G)[[t_1, \ldots, t_r]]$ for a certain
modification ${\widetilde{A}}(G)$ of the Burnside ring of the group $G$. We
give a formula for this Poincar\'e series of a collection of plane valuations
in terms of a $G$-resolution of the collection. We show that, for filtrations
on the ring of germs of functions in two variables defined by the curve
valuations corresponding to the irreducible components of a plane curve
singularity defined by a $G$-invariant function germ, in the majority of cases
this equivariant Poincar\'e series determines the corresponding equivariant
monodromy zeta functions defined earlier.
