A flat weave rug is any rug that is constructed without including any knots at all. Instead, the parallel running fibers that comprise the length of the rug (warp) and those that run along the width (weft) make up the whole surface of the rug. Flat weaving is a popular technique that has been used to create a number of rug types including some of the most popular and trendy rug styles in modern and Persian design.