  We present a new finite element method based on the formulation introduced by
Philippe G.~Ciarlet and Patrick Ciarlet, Jr. in [{\em Math. Models Methods
Appl. Sci., 15 (2005), pp. 259--571}], which approximates strain tensor
directly. We also show the convergence rate of strain tensor is optimal. This
work is a non-trivial generalization of its two dimensional analogue in [{\em
Math. Models Methods Appl. Sci., 19 (2009), pp. 1043--1064}]
