  We consider the problem of interaction of two oncoming shocks in plane
symmetry for a barotropic fluid. We establish a local in time solution after
the point of interaction, thereby determining the state behind the emerged
shocks which originate at the interaction point. The location of these shocks
in space time being unknown the problem constitutes a double free boundary
problem, i.e.~complete data for the problem is only given in a single point,
the interaction point. This article can be viewed as an extension of the
article arXiv:2112.15266 which deals with the reflection of a shock on a wall.
