The far-field time-dependent radiation pattern for an elastic plate excited by a transient point or line load is calculated. Comparisons are made between results calculated by both Timoshenko-Mindlin and classical plate theories. Such results have been obtained by others, but by viewing the results as a function of time and in a polar angle plane, one is better able to visualize and describe how the directional beam patterns are generated. The supersonic waves generated by the transient excitation give rise to a radiated field appearing as a precursor (with respect to the time of arrival of the sound emanating from the drive point) in a direction perpendicular to a Mach cone. The cone angle is determined from the ratio of the sound speed in the fluid to that of the flexural wave traveling with a velocity characteristic of the frequency at which the transient force spectrum has a peak. In those cases where an inhomogeneity, such as a dynamic system is attached to the plate, the time-dependent scattering pattern, in response to an ensonifying pulse, allows one to image and estimate the parameters of the scatterer.