This work provides a first version of a survey of explanation facilities implemented in AI-based design support software. The goal of the survey is to provide a comprehensive analysis that examines the existing approaches, prototypes, and tools, that aim at support of conceptual or concrete design phases in domains such as architecture or CAD and possess a certain explainability feature or component [...] component. The requirement for the approaches to be included in this survey is that they should be mainly based on AI or AI-based techniques, such as artificial neural networks, case-based reasoning, multi-agent systems etc. Each of the included approaches will be shortly described, with an emphasis on its explanation facility which then will be checked for certain criteria. In this paper, only a short selection