Abstract: Based on the Formex algebra and the mathematic mapping theory, a novel mesh generation technique for both two and three dimensional fluid flow field and the fluid-structure interface was presented. The virtual mesh system generated on the virtual regular polygon was mapped to the real mesh system by means of a family of the specific Formex algebraic functions. In the update technique for flow field mesh, the increment displacement mapping relationship and the reasonable random displacements along the fluid-structure interface were introduced, while the topology and data exchange format on the fluid-structure interface remained unchanged. Finally, some two/three dimensional interior and exterior flow fields were computationally investigated to verify the present technique and evaluate the quality of the initial and updated meshes.