We consider the problem of the existence of soliton-like self-gravitating cylindrically symmetric configurations of a classical spinor field with the nonlinearity F(S) (S = JOURNAL/gerg/04.02/00009364-200436070-00004/ENTITY_OV0619/v/2017-10-10T041305Z/r/image-pngΨ, F is an arbitrary function). Soliton-like configurations should have, by definition, a regular axis of symmetry and a flat or string-like geometry far from the axis (i.e., an asymptotically Minkowskian metric with a possible angular defect). It is shown that these conditions can be fulfilled if F(S) is finite as S → ∞ and decreases faster than S2 as S → 0. The set of field equations is entirely integrated, and some explicit examples are considered. A regularizing role of gravity is discussed.