A model is presented for the computation of the acoustic material signature for a line focus scanning acoustic microscope, based on a boundary element calculation and an electromechanical reciprocity identity. This identity is used to relate the voltage at the terminals of the microscope's transducer to the acoustic wavefields at the interface between the specimen and the coupling fluid. A Gaussian beam, launched in the buffer rod, is tracked through the lens and its matching layer. A model for the matching layer that is convenient for use with the boundary element technique is presented. The wavefields scattered from the surface of the specimen, including the leaky Rayleigh wave, are then calculated. Knowing the wavefields incident on and scattered from the specimen, the acoustic signature is calculated using the reciprocity relation. Results are presented for a defect free halfspace, and are compared with those of an analytical model and an experimental measurement.