An analysis approach is described which includes the effects of rock fabric strength anisotropy on wellbore instability. When drilling in geologically complex conditions - shown to be commonplace in the Andean foothills of South America - bedding-plane slippage, resulting from an unfavourable interaction between in-situ stresses, the well trajectory and bedding, is shown to cause severe instability for certain well trajectories. Case-history examples from the Pedernales field (Venezuela) and Cusiana field (Colombia) are presented which confirm the analytical predictions.