Hand dyeing generates artistic representations with unique and complex patterns. The aesthetics of dyed patterns on a cloth originate from the physical properties of dyeing in the cloth and the geometric operations of the cloth. Although many artistic representations have been studied in the field of non-photorealistic rendering, dyeing remains a challenging and attractive topic. In this paper, we propose a new framework for simulating dyeing techniques that considers the geometry of the folded cloth. Our simulation framework of dyeing in folded woven cloth is based on a novel dye transfer model that considers diffusion, adsorption, and supply. The dye transfer model is discretized on a 3D graph to approximate the folded woven cloth designed by user interactions. We also develop new methods for dip dyeing and tie-dyeing effects. Comparisons of our simulated results with real dyeing demonstrate that our simulation is capable of representing characteristics of dyeing.