Drained triaxial testing is challenging in low-permeability claystones (10−20 m2). This paper presents a method of testing low-permeability clay rocks in a standard triaxial cell. In this system, the resaturation of the specimen and the drainage conditions were enhanced by reducing the drainage length to 19 mm, the specimen radius. To do so, two geotextiles were placed around the top and bottom ends of the specimen, with no connection between them. Resaturation was hence performed by forcing water infiltration into the specimen from the upper and lower geotextiles, with a maximum infiltration length of around 19 mm, resulting in reasonable saturation durations. High-precision local measurements of radial strains were also achieved by ensuring direct contact between the LVDT rod and the specimen through the membrane. A poroelastic numerical calculation was carried out, and it was shown that, with these drainage conditions, a strain rate of 6.6 × 10−8 s−1 was satisfactory to ensure good drainage when shearing claystone specimens. After a check test made on a low-permeability sandstone with well-known mechanical characteristics, two tests were carried out to investigate specimens of the Callovo-Oxfordian claystone, a possible host rock for deep geological disposal in France. The results compare well with other published data from drained triaxial tests.