The use in irrigation construction of geotextile soils reinforced (strengthened) with fibrous materials, including cotton fibers waste of textile materials, requires strength assessment of these soils under tension and bending. Due to the low tensile and bending strength of soil, the load is born by the fibers reinforcing the soil. Direct methods to test tensile and bending geotextile soils are complex. It was proposed to evaluate the strength of geotextile materials through the strength characteristics of their components. Soils reinforced with textile waste cotton fibers are considered in the paper. To determine the strength of cotton fibers experimentally under the action of friction force only, a tensile test of cotton yarn consisting of cotton fibers was conducted. The diagrams of cotton yarn stretching obtained experimentally and the known diagrams of sandy soil compression are given in the paper. It was found that in the process of strain, both cotton yarn and soil change structurally. These changes are described by the change functions of their strain moduli, determined from considered experimental results in the form of graphs. Based on them, a method for assessing the strength of geotextile soils based on the general law of cotton yarn and soil strain is proposed. The possibility of using the formula obtained from this law for a particular case when determining and evaluating the strength of cotton yarns under tensile forces is shown. Therefore, it is recommended to use this formula in calculating the tensile strength of geotextile soils reinforced (strengthened) with waste textile materials used in innovative and modernized construction of irrigation reservoirs, canals, ditches, and reservoirs.