Within the scope of a spherically symmetric FLRW cosmological model we have studied the role of nonlinear spinor field in evolution of the universe. It is found that if the FLRW model given by the spherical coordinates the energy-momentum tensor (EMT) of the spinor field possesses nontrivial non-diagonal components. These non-diagonal components of EMT neither depend on the spinor field nonlinearity nor on the value of parameter k defining the type of curvature of the FLRW model. The presence of such components imposes some restrictions on the spinor field. The problem is studied for open, flat and close geometries. In doing so we exploited the spinor description of sources such as perfect fluid and dark energies. Some qualitative numerical solutions are given.
