We describe two morphological structures of barred galaxies with the help of numerical simulations. The first one is a feature seen in face-on barred galaxies, the ansae, probably very important dynamically speaking. The second one are the Boxy/Peanut bulges in disc galaxies. They have been associated to stellar bars, and are a result of the secular evolution of barred galaxies. We analyze their properties in a large sample of N-body simulations, using different methods to measure their strength, shape and possible asymmetry, and then inter-compare the results. Some of these methods can be applied to both simulations and observations. In particular, we seek correlations between bar and peanut properties, which, when applied to real galaxies, will give information on bars in edge-on galaxies, and on peanuts in face-on galaxies.