A procedure for the optimisation of hydrokinetic turbine array layout through surrogate modelling is introduced. The method comprises design of experiments, computational fluid dynamics simulations, surrogate model construction, and constrained optimisation. Design of experiments are used to build polynomial and Radial Basis Function surrogates as functions of two design parameters: inter-turbine longitudinal and lateral spacing, with a view to approximating the capacity factor of turbine arrays with inline and staggered layouts, each of which having a fixed number of turbines. For this purpose, two scenarios have been used as case studies, considering uniform and non-uniform free-stream flows. The major advantage of this method in comparison to those reported in the literature is its capability to analyse different design parameter combinations that satisfy optimality criteria in reasonable computational time, while taking into account complex flow-turbine interactions and different turbine types. (C) 2016 Elsevier Ltd. All rights reserved.