The article discusses the modification of a previously developed algorithm by the authors for solving systems involving non-linear supports, applied to the calculation of a pile raft foundation with a known dependency of pile settlement on load. The dependency of pile settlement on load was obtained experimentally, as a result of static testing of the pile in the ground. The proposed algorithm is based on a modification of the load compensating method using the finite element method in the form of the classical mixed method. The algorithm developed by the authors combines the advantages of the finite element method in the form of the classical mixed method and the load compensating method, taking into account that the function of the pile's elastic work in the ground is a piecewise-defined function consisting of three sections. When performing calculations the pile raft was loaded with a load applied according to the typical layout of load-bearing walls in a private low-rise house. The verification of the proposed algorithm was carried out by comparing the obtained results with the solutions of this problem obtained using common and verified software packages based on FEM in displacements, using both linear and nonlinear incremental calculation methods. The advantages provided by the finite element method in the form of the classical mixed method for linear and nonlinear calculation of a slab on piles are analyzed. The effectiveness and stability of convergence to the result of the load compensating method are demonstrated when using a calculation scheme with mixed unknowns.