For vibro-acoustic applications, a turbulent wall pressure fluctuations model was derived. The model is based on the resolution of the Poisson equation. The pressure is characterized in time and space through its spectrum in the pulsation wave-number domain. The developed model follows trends commonly observed using Corcos model in a large pulsation range but also shows new behaviours for low and high pulsations. The radiated noise due to turbulent wall pressure fluctuations is then computed in accordance with the form of the turbulent wall pressure spectrum. A specific computational methodology is proposed to perform the calculation without introducing limiting hypothesis on the radiated impedance.