To meet the increasing requirements of HCI researchers who are prototyping a variety of forms to create novel interfaces under a ubiquitous situation, we present WeaveMesh, a low-fidelity and low-cost rapid prototyping system that produces 3D objects in a mesh structure. Inspired by hand-weaving craft, WeaveMesh supports a highly customizable software platform, which is applicable for simulating and facilitating freeform surface constructions composed of woven lines arranged in a regular grid, which can serve as a guide for easy assembly. In addition, mobilizable connectors are suggested to support flexible assembly, which can be revised, recycled, and reused to facilitate short iterations. Furthermore, compared to common additive and subtractive techniques, WeaveMesh has a better balance between time and material saving. In this paper, we will introduce the system in detail and demonstrate the feasibility of the technique through various 3D models in the area of interactive media, products and architecture.