An ultra-strong tear resistant, cut resistant, puncture resistant bag having a high shear strength or modulus is provided by weaving ribbons of flat polypropylene sheet into a bag. The bag is formed by weaving a cylindrically shaped object, cutting the object transversely and sealing up one end to form the bag. The physical properties of the ribbon-woven bag easily accommodate holding refuse including bricks, wood with nails, glass and other refuse in a lightweight disposable bag. In an alternative embodiment, the ribbon-woven bag is overlain with sheets laminated to the exterior of the bag to provide a fluid-tight container.