Dynamic stresses in a tow wire caused by accelerations of the towing vehicle are considered for the case of rectilinear motion. The diameter of the wire is small compared to the wavelengths of the dominant Fourier components of the elastic waves, and the internal friction of the wire is neglected so that the one-dimensional wave equation may apply. It is shown that damping occurs in the wire material and in the interactions between the wire and the surrounding medium, and that maximum static and dynamic stresses occur at the towing end of the wire.