We develop a physical model of asteroid 1620 Geographos using Goldstone delay-Doppler radar images obtained August 1994 (Ostro et al. 1996, Icarus 121., 46-66) with resolution as fine as 75 m, and optical lightcurves obtained in 1969, 1983, and 1993-1994 (Magnusson et al. 1996, Icarus 123, 227-244). The data set admits a geometric ambiguity that precludes a unique model. Within this constraint, our model has maximum dimensions of (5.0, 2.0, 2.1) +/- 0.15 km and a volume of less than or equal to 8.8 km(3), equivalent to a sphere of less than or equal to 2.56 km diameter. The radar equivalent spherical albedo is greater than or equal to 0.12. The photometric solution provides Hapke parameters w greater than or equal to 0.22, g = -0.34 +/- 0.10, and <(theta)over bar> = 25 +/- 10 degrees with assumed values h = 0.02 and B-0 = 1.32. The spin state solution does not differ significantly from that of Magnusson et al, having lambda = 55 +/- 6 degrees, beta = -46 +/- 4 degrees, and P = 5.2233270 +/- 0.00000072 h. We identify seven main features in the delay-Doppler images and their corresponding locations on the model. (C) 1999 Academic Press.