We understand the maturity of an industrial enterprise in the context of the fourth industrial revolution as the state of the of internal and external conditions that support basic concepts of Industry 4.0 such as vertical and horizontal integration of production systems and enterprises or digital integration of engineering throughout the value chain. The ongoing trends of digitization and automation are causing many fundamental changes that will affect the entire area of logistics. On the way to Industry 4.0, intelligently controlled machines and robots will take over increasingly challenging tasks from humans. This is good news for logistics, whose complex processes with minimal standardization options are often limiting factors to expanding the automation of logistics and warehousing activities. An important aspect however is the company's readiness for the concept of Industry 4.0. Models of readiness evaluate the maturity of the company and are the main content of this paper, which is mainly of a search nature and compares the existing individual models. The analysis is based on knowledge of the main theoretical topics, which are described in the introductory part. Systematic research and evaluation of literature, comparison and analysis of models and interviews with experts are the basic development phase for the design of a new model of maturity which is focused on the evaluation of internal logistics processes. It is mainly a framework model with the main parameters, which is the subject of further development.