Industry 4.0 is a concept of automation and data exchange in manufacturing environment that combines advances of cyber-physical systems, Internet of Things, cloud computing, and cognitive computing. It is a highly networked system where only trustworthy elements are expected to participate in the network. Therefore, a possibility to have tools for indicating whether a particular node can or cannot be trusted in the network becomes an essential issue in successful functioning of cyber-physical systems in Industry 4.0. The paper proposes a trust handling framework as a base for such tools. The framework is based on knowledge derived from the related work in social sciences, information technology and computer sciences, and distributed sensing systems. The framework consists of several components that can handle initial and continuous trust issues concerning the nodes of the network of elements of cyber physical system of Industry 4.0.