Meshes for finite element analysis are formed by characterizing two or three dimensional bodies as passages for fluid flow. For a two dimensional body, the body perimeter is discretized and two portions of the perimeter are selected as inlet and outlet ends; the remainder serves as solid walls through which fluid cannot flow. A potential flow problem is solved for streamlines extending from inlet nodes to the outlet. Intersections of grid lines and streamlines determine interior inlet nodes on the surface. Quadrilaterals covering the surface are formed by connecting the nodes. For a three dimensional body, bounding surfaces are selected: one of the surfaces being an inlet surface and another of the surfaces being an outlet surface. The inlet is processed as described. A three dimensional potential flow problem from the inlet to the outlet is then solved. A series of grid planes are formed generally transverse to the three dimensional streamlines and progressing from the inlet to the outlet. The point of intersection of each streamline with the grid planes define flow nodes. For three dimensional meshes, neighboring nodes are connected to form quadrilaterals on each grid plane and these quadrilaterals are connected to quadrilaterals on neighboring grid planes to form hexahedra until the entire three dimensional body is filled.