We present an analysis of the mechanics of thin streams, which are formed following the tidal disruption of cold, low-mass clusters in the potential of a massive host galaxy. The analysis makes extensive use of action-angle variables, in which the physics of stream formation and evolution is expressed in a particularly simple form. We demonstrate the formation of streams by considering examples in both spherical and flattened potentials, and we find that the action-space structures formed in each take on a consistent and characteristic shape. We demonstrate that tidal streams formed in realistic galaxy potentials are poorly represented by single orbits, contrary to what is often assumed. We further demonstrate that attempting to constrain the parameters of the Galactic potential by fitting orbits to such streams can lead to significant systematic error. However, we show that it is possible to predict accurately the track of streams from simple models of the action-space distribution of the disrupted cluster.