A series of lateral tests conducted in a centrifuge on displacement piles in kaolin is used to examine the effects of pile shape, pile end-condition and clay overconsolidation on the lateral load transfer (p-y) curves in soft clay. These experimental tests are supported by finite-element analyses, which examine the responses of the circular, square and H pile sections used in the centrifuge tests. The experimental and numerical results reveal an important effect of pile shape on p-y curves, but no discernible effect of the pile end condition. These results also indicate comparable dependencies of net ultimate pressures on normalised depth and undrained shear strength. The findings enable development of a new formulation for p-y curves in soft clay, which incorporates the effects of pile shape and uses the triaxial compression consolidated undrained shear strength as the reference undrained strength.