A model of the weakfish, Cynoscion regalis, sound-production mechanism based on damped driven oscillators is presented. The weakfish "purr" consists of several short pulses of sound separated by intervals of no sound. Each pulse is produced by an individual simultaneous twitch of each sonic muscle causing swimbladder oscillations that radiate sound into the surrounding water. The sonic muscles are modeled as a stretched string with a time-varying tension force. The swimbladder is modeled as a highly damped, driven oscillator undergoing radial oscillations. Although the swimbladder functions as an impedance-matching device between the sonic muscles and the surrounding fluid, its transient response to the sonic muscle pulses includes frequencies that are not a part of the spectrum of the sonic muscle excitations. Differential equations of motion for the sonic muscles and swimbladder are given and are numerically solved to produce predicted waveforms matching those of measured weakfish sounds. The model leads to better understanding of the weakfish sound-producing mechanism and the effects of environmental and physiological factors on sound production. This model may also lead to a better understanding of sound production in other species, particularly other members of Family Sciaenidae, with similar mechanisms for sound production.