We analyze the swelling kinetics of constrained thin-plate gels using the linearized stress-diffusion coupling model proposed in the previous paper [Phys. Rev. E 69, 041402 (2004)]]. The gel is chemically clamped on the disk-like glass plates at the top and the bottom surfaces and can swell and shrink only along the thickness direction. We analyze how the top plate moves when a force is applied at a certain point on the top plate while the bottom plate is fixed. We predict that (i) the translation and the rotation of the top plate are described by a single exponential relaxation process, that (ii) the rotational relaxation process is three times faster than the translational one, and that (iii) when the force is applied to the edge, the displacement by the rotation is four times larger than that by the translation at the edge point where the force is applied. We also analyze how the gel deforms when it is clamped on the flexible film on which external load is applied.