The mean‐square displacement of a uniform, stretched string, restrained against lateral movement at the boundaries by springs, to a convected, random‐loading field has been investigated. A modal‐analysis technique based on Powell's method has been used, all crosscoupling terms being retained. The response is strongly affected by two parameters: the ratio of convection velocity to the wave velocity of the string (u/a) and the ratio of wavenumber of the excitation to wavenumber of the eigenfunction of the string (ke/ks). Modal response to a harmonic convected wave is greatest for all modes, except the first, when the ratios are both unity. For the first mode, the response is greatest when (u/a) approaches +∞ and (ke/ks) approaches 0 so that the product remains unity. The response is strongly affected by crossproduct terms, even though orthogonal eigenfunctions are used. Inclusion of the crossproduct terms in the calculations results in a mean‐square displacement that is less peaked at the center of the string but correspondingly higher toward the outer ends than if these terms had been neglected. The effect of the boundary flexibility is to increase the mean‐square displacement at all points of the string, and also to make the distribution of this displacement more uniform over the length.