This paper is the second part of an investigation on stress fields in an optimal elastic structure. In the first part of this research, Cherkaev and Kucuk (2001), we derived the necessary conditions for the stress field in optimal two-dimensional elastic structures and introduced a method to check whether a structure is optimal. In this paper, we turn our attention to conditions of the stress field in optimal three-dimensional elastic structures. We restate the necessary conditions for minimization of the stress energy for three-dimensional elasticity. We also show that the conditions are realized in optimal microstructures.