The West Antarctic Ice Sheet is drained primarily by five major ice streams, which together control the volume of ice discharged into the ocean across the grounding line. The grounding line of Kamb Ice Stream (KIS) is unusual because the ice stream upstream of it is stagnant. Here, a set of surface features--shore-parallel, long wavelength, low amplitude undulations--found only at that grounding line are examined and found to be "pinch and swell" features formed by an instability in the viscous deformation of the ice. When a relatively competent layer is surrounded by lower strength materials, particular wavelength features within the layer may be amplified under certain layer thickness and strain rate conditions. The undulations at KIS grounding line are possible due to the relatively large strain rates and particular ice thickness at that location. Several data sets are used to characterize the surface features. High resolution surface profiles are created using kinematic GPS carried on board a sled that was used to tow ice penetrating radar equipment. The radar data are used to examine the relationship between surface shape and basal crevasses. Additional surface profiles are created using ICESat laser altimeter observations. Repeat GPS surveys of a strain grid across the grounding line yields strain rate information. Analysis of repeat observations over tidal cycles and multi-day intervals shows that the features are not standing or traveling waves. Together, these observations are then used to evaluate the contributions of elastic and viscous deformation of the ice in creating the grounding line undulations.