This work investigates the contribution of sound diffraction in the acoustics of the ancient theatres, with reference to the theatre of Epidaurus. It is increasingly evident that in such theaters, the most important elements in the acoustic field are related to sound diffraction at the edges of the tiers, especially for the distant listener positions. For computational reasons, this study is limited to a 3D model of an elementary slice of the “koilon”, evaluated in the time and frequency domains. The analysis accounts for direct, reflected, diffracted and mixed reflection-diffraction paths, and calculates the theatre's acoustic response in various positions along the tiers. The model contains detailed parametrisation of the seat geometry and allows for comparisons by including or neglecting diffraction in the composite acoustic field. The contribution of the diffracted sound to the total sound field is evaluated through the estimation of energy-based acoustic parameters and the frequency response. The differences that occur in the typical acoustic parameters by accounting for diffraction are discussed. The ascending and descending components of the sound field are also analyzed regarding their composition and contribution to the predicted speech intelligibility.