With recent advances in digital computers, frequency response function (FRF) coupling has become a widely used analysis tool for a range of turbomachinery components, such as blades and discs, and this appproach has the distinct advantage of being based on a closed-form solution, thus not requiring a large number of elements to obtain reasonable accuracy. The problem, however, lies in the unavailability of tabulated expressions for geometries more complicated than straight beams or uniform discs, and hence the resulting model is rather too simplistic. This paper deals with the numerical evaluation of FRF matrices for twisted and rotating beams from knowledge of the governing differential equations in an attempt to refine the state-of-the-art stationary multi-stage uniform beam model of turbomachinery blading.