  We studied the behavior of nonlinear spinor field within the scope of a
static cylindrically symmetric space-time. It is found that the energy-momentum
tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal
components. The presence of non-diagonal components of the EMT imposes
three-way restrictions wither on the space-time geometry or on the components
of the spinor field or on both. It should be noted that analogical situation
occurs in cosmology when nonlinear spinor field is exploited as a source of
gravitational field given by Bianchi type-I cosmological model.
