The recent paper investigates the permeability of the washed sand soil and gypseous sand soil using a modified Oedometer cell. The gypseous sand soil sample is taken from a district in Al-Najaf city, Iraq. The soils are classified as “SP” according to the unified soil classification system. The gypsum content is 29% for gypseous sand soil. The samples are disturbed and remolded into the Oedometer cell with a density of 90% of the maximum Proctor dry density. The specific density samples are subjected to three different water heads: 0.80, 1.00, and 1.20 m. The first head (80 cm) is applied to the initial dry soil up to a saturated and steady state. While the other heads are subjected after the completion of the first one. Additional tests are performed on the nanoclay-treated soils with 5, 10, and 15%. The results of the permeability tests stated that there are a few differences in behavior between the two soils. The dry condition (first head) of the specimen is the longest duration of the test for both soils in the change from dry to saturated and then to steady condition. After adding 10% of the nanoclay, the permeability of the soil significantly decreases, and adding more is not worth it. In order to maintain the least amount of permeability reduction without interfering with the gypsum’s dissolving and washing processes in the soil, the water-head-to-specimen-thickness ratio must be less than 36.