Surface acoustic wave (SAW) devices are widely used as high quality factor filters for telecommunications. In recent years they have been investigated as sensors, which calls for application-specific electronic systems that interact with them. To design such circuits, it is important to understand the peculiarities of the devices, which may be a barrier for system designers. In this work, we explore different models that can be simulated in any circuit simulation environment, facilitating the creation of systems that interact with SAW delay lines, devices in which a signal is delayed by a constant time between piezoelectric transducers. The equivalent circuits of acoustic delay lines can be divided in two categories: a lumped-element model, based on frequency-dependent impedances implemented through the Foster and Mittag-Leffler theorems, and a distributed-element model, based on transmission lines. We compare qualitative frequency and time-domain characteristics among these categories so their limitations are clear, with the lumped-element model not being usable in the time domain due to its singularity at the center frequency. We also describe the process of implementation to achieve the model, while proposing a simple circuit block that can be included to represent perturbations on the device, which allows adjusting of the model response to different perturbations. Our model is also suitable for tests in distinct liquid media, provided that the parallel capacitor is fitted accordingly to model the electromagnetic wave induced in the device.