Transient leaky Rayleigh waves in a solid‐fluid half space system are studied using integral transform techniques. The obtained analytical solutions provide necessary theoretical background for optimization of air‐coupled ultrasonic detection in experiments. The leaky Rayleigh wave velocity can be obtained from the established characteristic equation. The leaky Rayleigh wave response under a normal point loading, which varies in time as a step function, is first derived. Closed‐form displacement and stress component expressions are then presented. The impulse responses owing to point loading can be obtained by taking differentiation of step responses; therefore, solutions to both arbitrary time‐varying and space‐varying transient impact loadings can be obtained by taking convolution in time and space domains. Numerical simulation (Finite integration technique) is used to verify the solution. © 2004 American Institute of Physics