Design of high quality factor (Q) micromechanical resonators depends critically on our understanding of energy losses in their oscillations. The Q of such structures depends on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. We study the dominant fluid interaction related losses, namely, the squeeze film damping and acoustic radiation losses in a drumhead microresonator subjected to different prestress levels, operated in air, to predict its Q in various modes of oscillation. We present a detailed research of the acoustic radiation losses, associated with the 15 transverse vibration modes of the resonator using a hybrid analytical-computational approach. The prestressed squeeze film computation is based on the standard established numerical procedure. Our technique of computing acoustic damping based quality factor Qac includes calculation of the exact prestressed modes. We find that acoustic losses result in a non-monotonic variation of Qac in lower unstressed modes. Such non-monotonic variation disappears with the increase in the prestress levels. Although squeeze film damping dominates the net Q at lower frequencies, acoustic radiation losses dominate at higher frequencies. The combined computed losses correctly predict the experimentally measured Q of the resonator over a large range of resonant frequencies. © 1992-2012 IEEE.