In this work, the transient ultrasonic waves radiated by a linear phased array transducer in a liquid then reflected at a liquid solid interface is studied. A model based on the Rayleigh integral is used where the reflection at the plane interface is considered by using the reflection coefficients for harmonic plane waves. The transient field is obtained by an inverse Fourier transform of the harmonic field. The obtained results highlight the different components of the ultrasonic field: the direct and edge waves as well as the longitudinal head waves or leaky Rayleigh waves. The temporal representation of these waves has been analyzed and discussed by the rays' model. Instantaneous cartographies allowed a clear description of all the waves which appear at the liquid-solid interface. The results have been compared to those obtained by using a finite element method.