The fracture behaviour of high-density polyethylene has only recently become the subject of comprehensive studies. Few of these studies have utilized a group of resins with systematic variation in molecular properties. In this work, a series of samples with controlled variation in chain structure have been prepared using commercial polymerization facilities. The fracture behaviour of these samples has been measured at both a constant rate of deflection and in static fatigue. Comprehensive statistical techniques were used to correlate these fracture results with the chain structure and morphology of the samples. Part I of this work presents the results for the work conducted at a constant rate of deflection. Both the fracture toughness and crack-growth rate were found to be most strongly dependent on the molecular weight of the resin. This is not an unexpected result. However, when variations in molecular weight are minimal, it was found that increasing the short branch content offers considerable scope for improving the fracture performance. Furthermore, longer short branches were found to be more effective at enhancing fracture behaviour. These results, which are of significant commercial importance, are interpreted in terms of existing models for the fracture process in polyethylene.