A detailed theoretical analysis is presented for calculating the surface acoustic wave (SAW) reflection coefficient of thin metallic layers. Based on this analysis, directions of propagation are classified as symmetric or asymmetric. An augmented scalar transmission line circuit model which contains a new lumped network element that accounts for asymmetry is introduced to describe SAW reflection and transmission through a strip. The resulting network model is used to analyze grating and transducer structures. Computed results based on this new network model are in excellent agreement with measured data, not only on devices oriented along symmetric directions, but also on devices which exhibit directivity due to asymmetric orientations. A simple procedure, based on physical arguments, is outlined for the identification of high directivity orientations. An algebraic construction is given which demonstrates that the coupling-of-modes (COM) modelling of gratings and transducers is derivable from the new network model. Approximate explicit analytical expressions, in terms of the network model, are given for the COM model parameters. The properties of pseudo-surface-waves are re-examined and a new high-velocity pseudo-surface acoustic wave (HVPSAW) is described. It is shown that this mode, not referenced in the SAW device literature, has a low attenuation along certain directions, and is thus very attractive for high-frequency low-loss SAW devices.