There are various streamlined schemes adopted in the flow channel structures of hydropower stations and pumping stations, which can be generalized as gradient flow channel structures. Based on previous engineering experience, the stress development characteristics of the gradient flow channel structures are different from those of other hydraulic concrete structures during the construction period. The development regularity of the temperature field and the stress field regarding concrete structures of this kind, with different forms of constraints applied, is studied and analyzed in depth through numerical simulation calculation. The results show that when both ends of the structure are constrained, the tensile stress will exceed the tensile strength of the structure concrete, and the penetrating cracks will easily occur. Whereas the stress state of the structure with both ends free of constraints is not significantly different from that with neither end being restricted. In addition, due to the large difference in cross-sectional dimensions between the thick end and thin end, their temperature field and stress field do not develop synchronously and the phase difference is about three months.