This work presents a new and simple formulation of a two-dimensional grid generation method that uses a special cubic spline algorithm developed to generate the analytical representation of arbitrary boundaries for two-dimensional domains. These cubic spline functions used for the fitting of points belonging to a boundary are special because they are generated based on a procedure that minimizes the length of the cubic spline functions defining the boundary. This avoids unwarranted inflection points common to cubic spline functions. Since the piecewise spline functions are cubic, they can easily accommodate contours of any shape, giving an analytical representation for the boundaries. The streamlines are constructed based on the boundaries generated by the spline model and the potential lines are built using the orthogonality principle. This mesh-generating model was developed for a two-dimensional two-phase computational fluid dynamic (CFD) model to study oil spills. The model, however, can be extended to three dimensions and some comments are presented in Section 3. (C) 2006 Elsevier Ltd. All rights reserved.