This work looks into the behaviour of the twill weave woven fabrics during relaxation (when the weaving tension is released). Ten, 50-metre rolls of twill weave woven fabrics were produced. The fabrics were marked in a rectangular form at the weaving loom. After 48 hours of relaxation, the new shapes and sizes were recorded. The shapes of almost all of the samples were changed to parallelogram, even though they differed in size. The work showed that the manner of fabric deformation during relaxation depends upon the fabric structure. It indicates that contraction due to relaxation of the twill weave causes the woven fabric to skew. in the direction of the twill. The quantity of the skewness is related to the float length and the twill type. Fabrics with longer float length have higher skewness.