A cross-linked polymer network immersed in a solvent will absorb molecules from its surroundings, leading to transient swelling. Under the constraint of a semi-permeable membrane, the system will swell less and generate a larger internal pressure in return, a system rarely analyzed to date. We use a nonlinear poroelastic theory to model the kinetics of swelling under mechanical constraint. We find the simulation results agree well with our experimental data using hydrogel beads made of a mixture of 3-sulfopropyl acrylate potassium salt and acrylamide, bathed in water. Understanding and predicting the response speed and the actuation stress developed during the swelling of constrained hydrogels can guide the design of polymer-based soft actuators with unusually high strength.