Experimental research of the moisture sorption process of 12 typical filaments used for FFF was performed in atmospheres with a relative humidity from 16 to 97% at room temperature. Materials with high moisture sorption capacity were revealed. Fick’s diffusion model was applied to all tested materials, and a set of sorption parameters was found. The solution of Fick’s second equation for the two-dimensional cylinder was obtained in series form. Moisture sorption isotherms were obtained and classified. Moisture diffusivity dependence on relative humidity was evaluated. The diffusion coefficient was independent of the relative humidity of the atmosphere for six materials. It essentially decreased for four materials and grew for the other two. Swelling strain changed linearly with the moisture content of the materials and reached up to 0.5% for some of them. The degree of degradation of the elastic modulus and the strength of the filaments due to moisture absorption were estimated. All tested materials were classified as having a low (changes ca. 2–4% or less), moderate (5–9%), or high sensitivity to water (more than 10%) by their reduction in mechanical properties. This reduction in stiffness and strength with absorbed moisture should be considered for responsible applications.