The evolution of packets of water waves described by the long‐wave limit of the Davey–Stewartson equations is considered. The stationary one‐dimensional kink solutions are analyzed with respect to transverse perturbations. They are shown to be stable when surface tension can be neglected. To demonstrate this, the two‐dimensional inverse scattering transform found by Anker and Freeman is applied. The present stability analysis supplements previous investigations in the long‐wavelength limit of water waves where finite depth effects have been ignored.