The concept of predictive maintenance using permanent sensors that monitor the integrity of an installation is an interesting addition to the current method of periodic inspections. Guided wave tomography has been developed to map the wall thickness using the travel times of guided waves. The method has been demonstrated for straight pipes. The extension of this method to bends is not straightforward because natural focusing occurs due to geometrical path differences. This yields a phase jump, which complicates travel time picking. Because ray-tracing is no longer sufficient to predict the travel times a recursive wave field extrapolation has been developed. The method uses a short spatial convolution operator to propagate a wave field through a bend. The method allows to calculate the wave field at the detector ring, including the phase jump as a consequence of the natural focusing. The recursive wave field extrapolation is done in the space-frequency domain. Therefore dispersion effects can be included easily in the forward modeling. Comparison with measurements shows the accuracy of the method. The tomographic reconstruction is based on the wave field extrapolation kernel.