In this paper we consider concircular vector fields of manifolds with non-symmetric metric tensor. The subject of our paper is an equitorsion concircular mapping. A mapping $f:\Bbb{GR}_N\to\Bbb G\bar\Bbb R_N$ is an equitorsion if the torsion tensors of the spaces $\Bbb{GR}_N$ and $\Bbb G\bar\Bbb R_N$ are equal. For an equitorsion concircular mapping of two generalized Riemannian spaces $\Bbb{GR}_N$ and $\Bbb G\bar\Bbb R_N$, we obtain some invariant curvature tensors of this mapping $\underset\theta\mathop Z$, $\theta=1,2,\ldots,5$, iven by equations (3.14, 3.21, 3.28, 3.31, 3.38). These quantities are generalizations of the concircular tensor $Z$ given by equation (2.5).