The dynamical evolution of stellar clusters is driven to a large extent by their environment. Several studies so far have considered the effect of tidal fields and their variations, for example, from giant molecular clouds, galactic discs or spiral arms. In this paper, we will concentrate on a tidal field whose effects on star clusters have not yet been studied, namely that of bars. We present a set of direct N-body simulations of star clusters moving in an analytic potential representing a barred galaxy. We compare the evolution of the clusters moving both on different planar periodic orbits in the barred potential and on circular orbits in a potential obtained by axisymmetrizing its mass distribution. We show that both the shape of the underlying orbit and its stability have strong impact on the cluster evolution as well as the morphology and orientation of the tidal tails and the substructures therein. We find that the dissolution time-scale of the cluster in our simulations is mainly determined by the tidal forcing along the orbit and, for a given tidal forcing, only very little by the exact shape of the gravitational potential in which the cluster is moving.