In this work, the linear swelling of four samples of natural clays was evaluated, using poly(propylene glycol) bis(2‐aminopropyl ether) Mfalse¯n~230 g mol−1 (PEDA‐230) and Mfalse¯n~400 g mol−1 (PEDA‐400) as shale inhibitors for water‐based drilling fluids, in comparison to a commercial shale inhibitor. The swelling kinetics was described by a semiempirical equation. A correlation was found between the cation exchange capacity of the clays and the diffusion kinetic constant of the inhibitors. Increased molar mass of PEDA favored swelling inhibition. The swelling inhibition was also evaluated by rheology, and the results were in agreement with the linear swelling tests. Scanning electron microscopy demonstrated the occurrence of microfractures on the clay surface after water contact, as well as the adsorption of the different shale inhibitors on the clay surfaces after contact with the aqueous inhibited fluid. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47661.