The Koyna Earthquake of December 11, 1967, caused the Koyna Dam to develop horizontal cracks both on the upstream and downstream faces in a number of monoliths(1, 10). The cracks were especially severe at elevations where abrupt change occurred in the slope of the downstream face. Cracks in dams create geometric nonlinearities, even though material properties are assumed to remain linear. Thus, the response problem becomes nonlinear. The normal mode super-position approach becomes difficult, and a direct numerical integration of the equations of motion provides a more attractive approach. For this study the numerical integration was performed using a fourth order Runge-Kutta method. In this paper a method is developed for formulating an approximate mathematical model of a cracked dam, and the behavior of Koyna Dam under earthquake forces is in- vestigated.