This work describes a generative method for the exploration of product shapes in the conceptual design stage. The method is based on three concepts: the notion of grammars to capture product appearance, the implementation of sketching transformation rules to produce design variations and the use of a parametric modeller to build shapes. We represent product solutions as 3D sketches using combinations of basic shapes arranged in simple and schematic product structures. This procedure allows creating many varied configurations with a minimal number of shapes, and facilitates the adaptation of the generative model to different products. The performance of the method is demonstrated through several examples from the literature. •A generative method for aesthetic shape exploration in product design is proposed.•The model generates a high number of variations and may adapt to different products.•The method focuses on the visual appearance of products.•It includes several sketch-related creative strategies (reformulation, analogy …).