The aim of the paper is to present the concept of maturity model for evaluation and continuous improvement of business and managerial capabilities that sustainably increase the resilience of logistics processes and the supply chain to severe and unpredictable disruptions. The development of presented model is a reaction on research gap consisting in the absence of a maturity model for building resilience in logistics and supply chain processes. Presented model also aims to overcome shortcomings of standard logistics maturity models, which are obsolescence over time, high subjectivity of assessment, absence of managerial competencies and lack of direct link to sustainable business performance. The research is also a response to the increasing number of serious and unpredictable crisis events in the current turbulent business environment, which significantly disrupt logistics processes and supply chains of industrial companies. The ultimate goal of whole research effort is to develop a tool that will help companies effectively deal with the increasing number of severe and unpredictable crisis events disrupting their logistics processes and supply chains. This goal will be achieved by development of a SCM resilience enhancing capacities maturity model.