Abstract: Some important concepts relating to the flattened Gaussian beams(FGBs),such as the field distribution and beam width, are analyzed physically. The twodimensional(2D) FGB is extended to the threedimensional(3D) case,and the 3D symmetrical transformations, inclu ding equal beam widths in x and y dimensions and equal curvature radii at a z plane, are studied in detail.