Abstract: The dynamics of timed continuous Petri nets under infinite server semantics can be expressed by a piecewise linear system with polyhedral regions. In this talk, Petri nets with symmetries are considered where symmetry is understood as a permutation symmetry of the nodes. I will show that if a Petri net has got such a structural symmetry, then this symmetry will also appear in the corresponding piecewise linear system and, therefore, also in its solutions. This allows to apply results from equivariant dynamical systems theory which can be taken advantage of, both for a qualitative and a quantitative analysis of the system. One consequence is that it is possible to identify equivalent regions meaning that they exhibit effectively the same dynamics. The symmetry in the vector field also makes it possible to identify flow-invariant subspaces just from the knowledge of the symmetry of the net. This both contributes to a better understanding of the dynamics and allows to transform the system to a lower dimensional reduced system by restricting the dynamics to these invariant subspaces.