Rectangular barrettes are increasingly being used to support large-size and heavy-duty structures, but the interaction among barrettes, soil, and cap has rarely been studied theoretically. This paper presents an approximate three-dimensional semi-analytical method for the analysis of load–displacement behaviour of single barrettes, barrette groups, and barrette–soil–cap interaction systems. A unique feature of a barrette, which distinguishes it from a circular pile, is its nonaxisymmetrical mechanical behaviour. To take into account this feature, both the barrette–soil and the cap–soil interfaces are discretized. Mindlin's solution is adopted to define the load–displacement relationship of the soils next to the barrette and the cap. By assuming the deformation compatibility at the barrette–soil and cap–soil interfaces, the load–displacement relationship of the soils is incorporated into the static force equilibrium conditions in the interior of the barrette and cap structures. In this way, governing equations in finite difference form are derived for obtaining the load–displacement response of the barrette–soil–cap system. The proposed method is verified by comparing the calculated results for a group of square piles using other existing methods. In addition, some factors such as barrette shape, barrette spacing, and barrette group layout and finite-layer depth, which influence the response of the barrette–soil–cap system, are investigated.Key words: elasticity, foundations, numerical modelling, piles, theoretical analysis.