The aim of the herein work is to estimate the swelling behavior of hydrogels through computational simulation by the lattice Boltzmann method. Multi-relaxation-time scheme is considered because of the effective diffusion coefficient changes as function of the water concentration during the swelling phenomenon. The lattice Boltzmann method allows us to employ dimensionless measurements of length and mass. A cylindrical sample of interpenetrating polymer network (IPN) hydrogel and a parallelepipedal sample of copolymeric hydrogel were synthesized to perform adsorption isotherm tests that were used to validate the values achieved by computational simulations. Hydrogel samples of cylindrical and parallelepipedal shape were simulated by D2Q9 model for a two-dimensional domain considering axisymmetric symmetry and by D3Q7 model for a three-dimensional domain. Grid (or lattice) convergence studies were done in order to guarantee numerical accuracy. Excellent correlations were achieved between the values obtained using the lattice Boltzmann method against experimental data. It can be concluded that the method described in this work can simulate the swelling behavior of hydrogels samples with cylinder and parallelepiped shapes.