A major problem before seismologists, earthquake engineers and exploration geophysicists engaged in seismic exploration is how to synthesize seismograms for realistic earth models. We report here one of our experiences in attempting such problems by evaluating the integrals of the formal solutions numerically. The solution to the problem of generating synthetic seismograms is required by seismologists to interpret the observed seismograms for deep earth structure and the earthquake source and by exploration geophysicists for shallow earth structures in areas likely to hold economic deposits of minerals, notably petroleum. Earthquake engineers are interested in synthetic seismograms for a number of reasons, chief among which is the need to predict ground motion to be expected over realistic earth models in response to earthquake induced excitation so that suitable safety provisions may be incorporated economically in the design of important man-made structures. Although the recent trend in earthquake engineering is to represent observed ground motion using statistical models, deterministic synthetic seismograms should provide useful constraints. In support of this remark we cite the observation that strong ground displacements computed as functions of time from observed accelerograms (see for example, Housner, 1970) are reasonably smooth.