In this paper, we propose an Inductive Design Exploration Method (IDEM) which can be used to design materials and products concurrently and systematically. IDEM facilitates hierarchical materials and product design synthesis, which includes multi-scale material structure and product analysis chains, and uncertainty in models and its propagation through the chains. In this method, we sequentially identify a ranged set of feasible specifications, instead of an optimal point solution in each segment of a hierarchical design process. The feasible spaces are searched from top-level design requirements to product and materials specifications taking into account propagated uncertainty. Strategies for parallelizing computations and achieving a robust solution for uncertainty in models are also addressed. The method is demonstrated with a simple example of designing a clay-filled polyethylene cantilever beam.