An attempt was made to distinguish aspects of the shape of rock particles, and to discover by analysis and empirical considerations the most appropriate parameters for describing these aspects. The shape of a rock particle can be expressed in terms of three independent properties: form (overall shape), roundness (large-scale smoothness) and surface texture. These form a three-tiered hierarchy of observational scale, and of response to geological processes. Form can be represented by only two independent measures from the three orthogonal axes normally measured. Of the four pairs of independent measures commonly used for bivariate plots, the two sphericity/shape factor pairs appear to be more efficient discriminators than simple axial ratios. Of the two, the most desirable pair is the maximum projection sphericity and oblate-prolate index for both measures show an arithmetic normal distribution for the range investigated. A measure of form that is independent of the three orthogonal axes, and measures derived from them, is the angularity measure of Lees. Roundness has measures of three types, those estimating average roundness of corners, those based on the sharpest corner, and a measure of convexity in the particle outline. Although each type measures a different aspect, they are not independent of each other. Only roundness from corners is considered in detail. As neither average nor sharpest corner measures are inherently more objective or more quantitative, purpose should determine which is more appropriate. Of the visual comparison charts for average roundness, Krumbein's appears best. The Modified Wentworth roundness is the most satisfactory for estimating roundness from the sharpest corner. The Cailleux Roundness index should not be used because it includes aspects of roundness and form. Shape is a difficult parameter to use for solving sedimentological problems. Even the best of the commonly used procedures are limited by observational subjectivity and a low discriminating power. Unambiguous interpretation of particle shape in terms of source material and processes will always be made difficult by the large number of natural variables and their interactions. For ancient sediments satisfactory results can be expected only from carefully planned studies or rather unusual geological situations.