The details of a plastic-damage model are explained in the context of a three-dimensional formulation. In particular the procedure for stress calculations is described for the more challenging cases, of which large crack option is considered. Similarly, algorithmic tangent stiffness is discussed under these circumstances. Based on these theories, a special-purpose finite element program is enhanced, and is subsequently utilized to study the non-linear dynamic response of the Koyna Dam during the excitations of the Koyna earthquake in 1967. It should be mentioned that non-linear analysis is carried out using two different alternatives and the responses, including the extent of damages, are compared. These options correspond to initial stiffness and full Newton-Raphson algorithms. Furthermore, it should be emphasized that three-dimensional modelling is adopted herein to simulate a plane stress state. The considered idealization corresponds to the three-dimensional modelling of a slice through a typical monolith with 1m thickness under almost full reservoir conditions. In this respect the present study can be considered as the initial major verification for this kind of modelling, which can ultimately be applied to the study of the non-linear response of concrete arch dams.