Studying the acceptance of exoskeletons in industry has gained increased attention. Exoskeletons (wearable support devices) are envisioned to alleviate heavy work. Examining what factors influence the use of exoskeletons is important, because influencing these factors could positively contribute to the adoption of industrial exoskeletons. The factors identified in this paper have been systematically derived from empirical research with (potential future) end users, most of whom have tried on an exoskeleton. Our framework with factors influencing the acceptance of industrial exoskeletons can be used during the (ideally iterative) design, (re)development and evaluation phase of new or existing exoskeletons. This could improve the quality of exoskeletons since this allows designers to already consider acceptance factors early in the design process instead of finding out what is important late in the design process during (field) testing. In turn, this might accelerate the adoption of exoskeletons. Also, our framework can be used to study the ongoing introduction of exoskeletons at work since it also addresses policy decisions companies interested in implementing exoskeletons should consider.