Flexoelectric effect and dielectric effect in uniform lying helix (ULH) cholesteric liquid crystals under cell boundary conditions of periodic anchoring at the bottom and vertical anchoring at the top are studied. They can be quantitatively analyzed by theoretically simulation of the polar angle and the tilt angle. It is found that a good ULH texture can be formed inside under periodic boundary conditions and the bulk director is not affected by the surface anchoring strength. The induced rotation angle of the helical axis by the flexoelectric effect is slightly non-uniform with the position, and the coupling of the flexoelectric effect and dielectric effect increases the inhomogeneous change. Our results will provide an accurate theory basis for the formation of a good ULH texture and the influence of dielectric effect on the optical axis.