This paper presents a time-domain model for the prediction of acoustic field in an air-coupled, non-contact, ultrasonic surface wave scanner, which includes an air-coupled Emitter, the Propagation space, and an air-coupled Receiver (EPR). The computation is divided into three steps, with each step being modeled in the time domain by its spatio-temporal transfer function. The latter are then used in turn, to find the pulse response of the overall system. The model takes the finite size of the aperture receiver, the attenuation in both air and the tested solid sample, as well as the electric response of the emitter-receiver set he into account. The attenuation is characterized by a causal time-domain Green's function, allowing wideband attenuation of a lossy medium, obeying the power law αω=α0ωη,0⩽η⩽2, to be used. The model is implemented numerically using a Discrete Representation approach. It is then validated quantitatively by comparing the predicted acoustic field with experiment. The prediction error for three typical field features, the system's impulse response, the on-axis field distribution, and the directivity pattern, is globally smaller than 3%. In order to obtain this high level of accuracy in the model, the parameters characterizing the solid sample used during the experiment were measured experimentally, with a specifically developed experimental setup. Overall, the proposed model is approximately 100 times faster than 3D FEM with an equivalent spatio-temporal resolution. In parallel, a simplified model is proposed, which neglects the attenuation in air and assumes the emitter inclination angle to be perfectly adjusted. This approach makes it possible to further shorten the computational time by a factor of about ten, whilst maintaining good accuracy. Thanks to its computational efficiency, the proposed model can be used to formulate various recommendations concerning the scanner settings, in particular the inclination angles of the emitter and receiver, and their distance from the sample.