In computing the mean‐square generalized force (or the joint acceptance) of a structure undergoing excitation by random pressures, approximations can often be made that will greatly reduce the computational effort and that do not affect the accuracy significantly. It is shown that the mean‐square generalized force has an upper bound that is easy to compute, useful for irregular‐mode shapes or correlation functions. In addition, it is shown that spatial variations in the mean‐square pressure of an antisymmetric nature over the surface do not affect the joint acceptance, while the effect of symmetrical variations is small.