This paper investigates the modelling of coupled soil-structure interaction problems by domain decomposition techniques. It is assumed that the soil-structure system is physically partitioned into soil and structure subdomains, which are independently modelled. Coupling of the separately modelled partitioned subdomains is undertaken with various algorithms based on the sequential iterative Dirichlet-Neumann sub-structuring method, which ensures compatibility and equilibrium at the interface boundaries of the subdomains. A number of mathematical and computational characteristics of the coupling algorithms, including the convergence conditions and choice of algorithmic parameters leading to enhanced convergence of the iterative method, are discussed. Based on the presented coupling algorithms a simulation environment, utilizing discipline-oriented solvers for nonlinear structural and geotechnical analysis, is developed which is used here to demonstrate the performance characteristics and benefits of various algorithms. Finally, the developed tool is used in a case study involving nonlinear soil-structure interaction analysis between a plane frame and soil subjected to ground excavation. This study highlights the relative performance of the various considered coupling algorithms in modelling real soil-structure interaction problems, in which nonlinearity arises in both the structure and the soil, and leads to important conclusions regarding their adequacy for such problems as well as the prospects for further enhancements.