The theory and application of plastic anisotropy have extensively developed in the main field of sheet metal forming. Round tubes and bars are generally used for tube forming and forging; they exhibit plastic anisotropy similarly to sheets. In this paper, assuming that these materials show anisotropy with three cylindrical orthogonal symmetry axes, r, θ and z, we used the simple anisotropic criterion proposed by Hill in 1948 as follows: 2C2 = F (σθ- σz)2 + G (σz- σr)2 + H (σr- σθ)2. In the tube materials, the ratios εθ/εr = F/G and εθ/εz = H/G are not necessarily equal to unity. For a tube of A6063 in JIS as an example, F/G = 0.55 and H/G = 0.69 were determined by a tube tensile test and a tube wall compression test, respectively. In the bar materials, we theoretically showed that anisotropy affects the mean stress in the tensile/compression test. Also, by a semi-cylinder compression test, for a round bar of A2017-F in JIS as an example, F/G = 0.37 was determined. Moreover, in the ring compression test for determining frictional coefficient, we found using FE analysis that anisotropy and friction affect the reduction in internal diameter.