It has been observed that high-velocity coolant flowing through the channels of a parallel-plate fuel assembly will at times cause large deflections of the assembly plates. In the present investigation, hydraulic equations are coupled to the plate equations along the entire length of the assembly. Solution of these coupled equations was accomplished by changing the differential equation developed from plate theory into a non-linear integral equation. The classical method of successive approximations was used to evaluate the integral equation numerically. Numerical results show that: 1) plate deflections take place along the entire length of the plate, and 2) local reductions in channel cross section are further reduced by elastic deflections of the plate.