An automatic mesh generation scheme with triangular finite elements on three-dimensional surfaces has been developed. The surface triangulation process is performed as follows. To begin, surfaces with key nodes are transformed to two-dimensional planes and the meshes with triangular elements are constructed in these planes. Finally, the constructed meshes are transformed back to the original 3D surfaces. For the mesh generation, an irregular mesh generation scheme is employed in which local mesh densities are assigned by the user along the boundaries of the analysis domain. For this purpose a looping algorithm combined with an advancing front technique using basic operators has been developed, in which the loops are recursively subdivided into subloops with the use of the best split lines and then the basic operators generate elements. Using the split lines, the original boundaries are split recursively until each loop contains a certain number of key nodes, and then using the basic operators such as type-1 and type-2, one or two triangular elements are generated at each operation. After the triangulation process has been completed for each meshing domain, the resulting meshes are finally improved by smoothing process. Sample meshes are presented to demonstrate the versatility of the algorithm.