The ultrasonic pulse-echo method aims to use the measured echo-signals to characterize defects — their location, orientation and size. The solution of this inverse problem requires the availability of good models of the forward problem, that is an understanding of radiation and reception of ultrasonic waves by realistic transducers as well as of the processes of scattering by arbitrary defects. This in itself is very complicated and requires simplifications and approximations. This paper aims to extend a previous model dealing with the case of propagation in fluids [1,2]. Modeling the actual propagation in solids as a propagation in fluids is a simplification commonly made in the considerable literature. A solution for solids requires account to be taken of both compression and shear waves. Since the two types of wave propagate with different velocities, a solution for fluids is acceptable if the defect is sufficiently distant from the transducer, that is, if the arrival-times of the respective echoes are well separated in time. When this condition is not fulfilled, compression and shear waves as well as their mode-conversion at interfaces must be considered. The earlier solution for fluids has shown the paramount importance of transducer diffraction effects in the echo-forming mechanism. The solution explicitly used the impulse-response theory for calculating transducer diffraction effects both in radiation and reception. The first step to extend the work to solids was to dispose of a solution for the transient radiation in a solid medium. Such a solution has been developed. It is based on the approximation that Rayleigh and head waves contributions generated by the transducer are negligible at field-points of interest [3,4], i.e., the solution is suitable at field-points not too close to the interface where the transducer radiates. In using this solution for modeling the behavior of the transducer both in radiation and reception, the complete solution for radiation, scattering and reception will not apply for modeling echo-responses from defects close to or at the interface, e.g., surface breaking cracks. Despite this fundamental limitation, number of practical cases of pulse-echo method may be modeled.