We investigated the synthesis and structure-property behaviors of two types of vegetable-oil polyols (soy oil and castor oil) and their use in viscoelastic (VE) polyurethane foams (PUFs). This article is the first in a two-part series. In this initial part, we principally address the dynamic mechanical analysis (DMA) behavior of these foams in conjunction with information on the cellular morphology, sol fraction, and rise and reaction temperature profile behavior (the latter two parameters were determined during the foaming process). Particular emphasis is placed on the DMA damping characteristics, which represent one of the most critical parameters in the application of VE PUFs. It is also shown that the damping characteristics could be modified in such foams by the variation of the isocyanate/hydroxyl (x 100) index, the addition of plasticizer, and in the case of soy polyols, the soy content. The frequency dependence of the VE PUFs is also briefly addressed. In the second article in this series, which directly follows this article, we further address the details of other relevant physical properties of these same foams in view of their applied nature. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 119: 2683-2697, 2011