In this paper, the application of the Equivalent Source Method (ESM) and the acoustical Boundary Element Method (BEM) for the prediction of the noise generated by an open diffusion flame is investigated. These acoustical methods have been coupled with a Large Eddy Simulation (LES) of the turbulent flow, which simulates the flow and combustion processes in a source region in the vicinity of the flame. Among the hybrid methods which are being used to predict the sound produced by turbulent flow, the ESM and BEM have the advantage that only one acoustic variable must be known at a surface surrounding the source zone (fewer data has to be processed) and that the far field can be directly computed. The sound power generated from two open diffusion flames have been calculated with both the ESM and the BEM, using the velocity distribution over cylindrical control surfaces, which enclose the source region. The results of the calculations are presented and compared with the measured sound power of the same flames. For one configuration good agreement between measurement and simulation at low and middle frequencies is obtained. Possible reasons for the differences for the other configuration will be discussed.