In this Letter we propose a rigorous and generalized approach for the design of integrated optical bent directional couplers (DCs) based on the coupled mode theory and super mode theory. The full vectorial finite-element method is used for the calculation of effective indices of optical modes propagating into the waveguides constituting the DCs. The flexibility and robustness of this general modelling approach is demonstrated by simulating several directional coupling configurations, as those based on cosine S-bend and double arc bent waveguides. Furthermore, some numerical results have been validated by comparison with the three-dimensional semi-vectorial beam propagation method.