Human endostatin is one of the better characterized endogenous angiogenesis inhibitors, and its ability to modulate vascularization of tumours could be of great therapeutic interest. These properties are not exclusive to the full-length protein, but are shared by some of its synthetic fragments. A number of research groups have partitioned human endostatin in different peptides and have investigated their activity, in order to collect a body of experimental data which could be important in shedding new light on their structure-activity relationships. It was also reported that a small active fragment can become inactive when contained in a larger fragment, revealing an apparent discrepancy in the experimental results. Very few studies have been devoted to the computational analysis of these systems and to the rationalization of their properties using molecular modelling. Through molecular dynamics simulations of human endostatin and of four synthetic fragments, we have been able to rationalize the experimental findings. In particular, we have identified a pattern consisting of six amino acids, namely R-R(G)-A-D-R-A, which appears to be an active epitope if it is properly exposed to the solvent. Interestingly, this pattern can be already present in sequential order in the primary structure, or it can be generated by the spatial approach of two groups of residues, far apart in the primary structure, as an effect of the peptide folding. Comparing the structural features and the time evolution of all the simulated peptides we provide a coherent explanation of their activity or inactivity.