Two sorts of dielectic absorption coming from the amorphous part are observed in each of the usual solid linear high polymers. The absorption of the high temperature (low frequency) side is called the αa-absorption and that of the low temperature (high frequency) side the βa-absorption.The shapes of the αa- and βa-absorptions are discussed both in experimental and theoretical ways with respect to the dependences of the width and the asymmetry of the absorption curves upon the degree of crystallinity and the chemical structure. Cole-Cole's parameter β and the parameter of the sech-law α are adopted in this paper for representing the characteristic features of the shape of the dielectric absorption curve semi-quantitatively. The shape of the αa-absorption is discussed at much higher temperatures than Tg and the shape of the βa-absorption at much lower temperatures than Tg, because the shape of the absorption curve scarecely changes with temperature at these respective temperature ranges.The observed results are as follows: (α.1) Cole-Cole's parameter β for the αa-absorption curve of the typical amorphous polymer takes the value of 0.7∼0.8, where β becomes a little smaller with the increase of the steric effect, at least for the polymers which have resemble chemical structures. The β of the polymer which seems to lie between the amorphous and the crystalline polymer (such as PVC and PAN) takes the value of 0.5∼0.6. The value of β decreases with the increase of the degree of crystallinity in the typical crystalline polymer and tends to the value of 0.2∼0.3. (α.2) The αa-absorption curve shows a little asymmetrical shape if it is plotted in logarithm of the frequency scale. The higher frequency side of the absorption curve is a little gentler than the lower frequency side for the amorphous polymer. With the increase of the degree of crystallinity, the αa-absorption curve becomes symmetric and, finally, the lower frequency side becomes gentler. (β.1) The β of the βa-absorption curve takes the value of 0.2∼ 0.4 irrespectively with the degree of crystallinity and with the chemical structure. (β.2) The shape of the βa-absorption is relatively symmetrical excepting the cases of aromatic polyesters.The theoretical expressions of the shapes of the αa-and βa-absorptions are derived. The calculation is made on the basis of the following mechanisms; that is, the αa-absorption is due to the segmental micro-Brownian motions of the main chains in the amorphous part and the βa-absorption is due to the local motions of the main chains in the amorphous part such as the local distortions of the chains in the frozen state. The agreements between the theory and the observations are satisfactory.