Three-dimensional finite-element analyses are performed to compute the interaction factors between two neighbouring piles, under both static and dynamic horizontal displacements. The fixed-head elastic piles are flexible, embedded in a homogeneous saturated clay stratum, and loaded under undrained conditions. Soil inelasticity and soil\u2013pile interface separation are modelled in a rational way. With the aim of improving fundamental understanding of pile\u2013soil\u2013pile non-linear interaction mechanisms, it is found that the effect of a loaded (\u2018source\u2019) pile on an adjacent (\u2018receiver\u2019) pile diminishes rapidly with increasing amplitude of imposed displacement, at a rate which depends on the angle of departure from the direction of loading between source and receiver piles. Gap formation at the back of a displaced pile affects the response of the group. Using the interaction factors developed, the behaviour of 2\u200a\u00d7\u200a2 and 3\u200a\u00d7\u200a3 pile groups is analysed and compared with the three-dimensional analysis of the whole group. Under static conditions the differences between front (\u2018leading\u2019) and back (\u2018trailing\u2019) piles are illustrated. Under cyclic dynamic conditions, the separation gap forms on each side of a pile alternately, leading to the peaks in stiffness diminishing, and leading to larger (than the elastic) group efficiencies. Superposition using proper non-linear interaction factors offers reasonable approximation, but only for moderate amplitudes of load, smaller than about one-half of the ultimate lateral pile capacity.