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A numerical method has been developed to study the effects of structural mistuning on the aeroelastic behaviour of turbomachinery cascades. The specific objectives of the work presented here were the following: A method was to be developed that can assess the major effects of structural mistuning in a cascade in sub- and transonic flow situations. The influence of mechanical and aerodynamic coupling between the blades as well as coupling between multiple modes for each blade was to be included. Accurate representations of the aerodynamic forces, taken from a modern three-dimensional unsteady aerodynamic solver were to be used. The method should be applicable for design use, meaning that it has to supply results quickly for a large number of configurations. The applicability and accuracy of the method was to be demonstrated by comparison of numerical results to available data from recent experiments. The influence of major parameters on the aeroelastic stability and on the resonant amplitude of representative test cases should be assessed. The approach used to achieve these goals is the combination of a linearised Euler method for the aerodynamic calculations with a modal reduction technique, where the structural properties of each blade are represented by only a few eigenmodes. The method is validated and applied to two test cases, comprising of a transonic compressor rotor and a high pressure turbine rotor. Both are representative of modern turbomachinery designs. The final conclusions of this work are: The newly developed method is capable to assess the dominant effects of structural mistuning in turbomachinery cascades, including the mechanical and aerodynamic coupling of adjacent blades and the aerodynamic coupling of multiple modes with arbitrarily complex modeshapes. In this method, the aerodynamic characteristics of the cascade are accurately represented using the generalised unsteady aerodynamic coefficients derived from a modern three-dimensional flow solver, applicable to and validated for both sub- and transonic configurations. The simplifications employed significantly contribute to the computational efficiency of the method, making it applicable for design purposes as well as for the assessment of large parametric variations or for statistical studies of stochastically mistuned configurations. The current method is successfully validated by a comparison of numerical to experimental data. The applicability and accuracy is demonstrated by the favourable agreement between measured and computed results. Based on these validations, the method is applied to study the influence of major parameters on the aeroelastic behaviour of the selected test cases. The results show a wide range of phenomena, dependent on the type and strength of mistuning, frequency, modeshape and interblade phase angle. The results highlight the close inter-dependence of the aeroelastic stability derived from the eigenvalue analysis and the resonant amplitudes derived from the forced response analysis.