This paper deals with the solution of the Riemann problem for the system of the Euler equations in a duct of variable cross section, which is one of the simplest examples of a non-conservative system. The work presented is based on an the observation that the governing system is locally equivalent to some conservative system, and therefore, in spite of the fact that shocks satisfy (locally) a usual entropy criterion, the solution to the Riemann problem for certain initial conditions may not be unique. For the selection of a physically relevant solution, a criterion has been proposed whose justification is given by comparing the 1D exact solution with the computation of the Euler equations in a duct of corresponding geometry averaged over the cross section.