Forward modeling of ground penetration radar is developed using exact ray-tracing techniques. Structural boundaries for a ground model are incorporated via a discrete grid with interfaces described by splines, polynomials, and in the case of special structures such as circular objects, the boundaries are given in terms of their functional formula. In the synthetic radargram method, the waveform contributions of many different wave types are computed. Using a finely digitized antenna directional response function, the radar cross-section of buried targets and the effective area of the receiving antenna can be statistically modeled. Attenuation along the raypaths is also monitored. The forward models are used: (1) as a learning tool to avoid pitfalls in radargram interpretation, (2) to understand radar signatures measured across various engineering structures, and (3) to predict the response of cultural structures buried beneath important archaeological sites in Japan.