We generalized the semiclassical path integral method originally used in the DyakonovPerel mechanism to study the spin relaxation of the ElliottYafet mechanism in low-dimensional systems. In quantum wells, the spin properties calculated by this method confirmed the experimental results. In two-dimensional narrow wires, size and impurity effects on the ElliottYafet relaxation were predicted, including the wire-width-dependent relaxation time, the polarization evolution on the sample boundaries, and the relaxation behavior during the diffusiveballistic transition. These properties were compared with those of the DyakonovPerel relaxation calculated under similar conditions. For ballistic narrow wires, we derived an exact relation between the ElliottYafet relaxation time and the wire width, which confirmed the above simulations.