A study of the expression for the response power spectral density of linear systems to random pressures shows that the response problem essentially reduces to evaluating the joint acceptance of the system with the pressure field. A novel method using a coordinate transformation is presented. This method enables one to determine very simply the joint acceptance of a beam that has arbitrary end constraints with a pressure field that has a spatial‐pressure correlation function that is easily described mathematically. The joint acceptance of a simply supported beam with a reverberant acoustic field as a function of mode number and nondimensionalized frequency parameter (beam length/acoustic wavelength) has been computed for the first 16 modes. An engineering approximation for the joint acceptance of a simply supported flat plate with a reverberant acoustic field is obtained from the beam results. The method is also used to determine very simply beam and flat‐plate joint acceptance with a turbulent‐boundary‐layer pressure field and with an acoustic plane wave.