The influence of microstructure and temperature on the initiation of yield stress and strain of high density polyethylene are examined using a set of linear and branched polyethylenes. The polymers were crystallized in different ways in order to get samples covering the range of crystallinity 0.5 <= X-c <= 0.8 and crystallite thickness 8 nm <= L-c <= 29 nm. In contrast to the conventional macroscopic yield strain and stress, the initiation strain epsilon(yi) and stress sigma(yi) were estimated from the macroscopic stress-strain curves at the onset of local plasticity as judged from in situ WAXS experiments upon tensile deformation. Phenomenological linear relation was observed between sigma(yi) crystallinity at each draw temperature T-d. The dislocation model was applied to check the correlation between sigma(yi) and crystal thickness. In order to also account for the chain topology, namely the concentration of stress transmitters ST, a modified Eyring's approach was proposed. This modelling provides a good prediction the sigma(yi) dependence on Lc and ST in the context of thermally activated rate processes. Finally, anelastic stress gauge, sigma(cr)(c), was determined from local strain measurements in crystals at the same local strain as for (sigma(yi). This critical elastic stress at initiation of crystal plasticity displayed a good correlation with sigma(yi) at high crystallinity. However, sigma(cr)(c) was found to deviate from sigma(yi) with increasing T-d particularly at low X-c values. This finding was attributed to the activation of the crystalline mechanical relation that involves a significant drop of sigma(yi) with increasing T-d in the crystalline lamellae under shear yielding whereas it does not affect the theoretical sigma(cr)(c) elastic stress. (C) 2017 Elsevier Ltd. All rights reserved.