The dispersion and loss characteristics of groove guide with arbitrary shapes are analyzed with high-order finite element method. The effectiveness and the reliability of the method are verified by the experiments and the results obtained by other mehods. Groove guides with various groove shapes, such as reorangular, triangular, parabolic, elliptic and cosine functions are investigated systematically. The calculating results show that the dispersion of groove guide with different groove shape is almost the same; the loss characteristic is rather different, among them. V-shape groove has the lowest loss, which is about half of
the loss of rectangular groove guide. All the curves and .the data given in this paper can be used in designing the elements and circuits composed of the groove guide.