The Natural Gas Distribution sector is considered one of the most critical areas in which Industry 4.0 methodologies can be applied, as they form a part of critical infrastructure management where automation, information technology and high-tech solutions can offer high-level service. The paper aims to identify critical business processes that can substantially benefit from Industry 4.0 and Information Technology solutions in a Natural Gas Distribution Company which distributes Natural gas in Greece in Medium and Low Pressure.The research conducted identified the company’s business processes and highlighted these which are critical to its operation. Having identified the technological advancements in the Gas sector, the business processes that can benefit from Industry 4.0 and Information and Communication Technologies were recognized.The results revealed three critical business processes that can be radically improved: management of new customers’ connections, project management of works projects and network maintenance. Technological approaches that can transform these processes were identified to be a real-time collaborative CRM system, a real-time collaborative project management system integrated with an appropriate document management system, smart meters, sensors and actuators for real-time monitoring of important operational variables and a monitoring system which collects and generates consolidated information in a Control Room.Identification of the processes into which Industry 4.0 and information technologies can lead to the introduction of corresponding solutions, can increase operational efficiency of company’s network and minimise running costs. The research effort should be continued in order to achieve higher integration between business processes, Industry 4.0 concepts and Information Systems.