AbstractThe paper is a study of motions for which the stretching tensor is convected without diffusion. It is shown that the diffusion of the stretching tensor vanishes if and only if the right Cauchy‐Green tensor is equal to its value for a rigid motion plus twice the product of the initial stretching with the elapsed time. It is further proved that the only isochoric motions for which the diffusion of the stretching vanishes are rigid motions.