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1. Introduction. We describe two methods, relevant to the study of Saint-Venant's principle, for the derivation of decay estimates in a linear isotropic homogeneous elastic nonprismatic cylinder loaded by prescribed end displacements and with fixed curved lateral surface. The results and associated calculations are expressed in terms of integrals taken over plane cross sections of the cylinder rather than averages over partial volumes as in many previous discussions. (See, for example, Toupin [25], Oleinik and Yosifian [23], and Fichera [6,7]; other references to this and related issues may be found in the comprehensive survey by Horgan and Knowles [15].) A notable exception is the investigation by Biollay [1] who examines the three-dimensional semi-infinite prismatic beam with lateral sides held fixed and data specified over the base of the cylinder. (We also mention in this respect the study by Knowles [19] of the semi-infinite plane strip with lateral sides stress-free.) An exponentially decreasing decay rate is obtained which, of course, is a common feature of most studies of

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