Linenizing is most frequently done on paper products and its use on paper products goes back to the early part of the 20th century.
A paper roll is threaded between two hard rollers, usually made from steel. One or both of the steel rollers has a linen pattern engraved on it. As the nip pressure between the two hard rollers increases, the pattern from the engraved roller(s) is pressed into the paper. The end result is a pattern that looks like a linen table cloth or linen dress.
Various patterns and depths of those patterns have been developed throughout the years. Generally, the pattern is a series of vertical and horizontal lines with distances varying between those lines.