A new analytical model is developed for the prediction of noise from serrated trailing-edges. The model generalizes Amiet's trailing-edge noise theory to sawtooth trailing-edges, resulting in an inhomogeneous partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with finite element method for a variety of serrations at different Mach numbers. Results obtained using the new model predict noise reduction up to 10 dB at 90° above the trailing-edge, which is more realistic than predictions based on Howe's model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing-edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at ninety degrees above the trailing-edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.