Filler strips made of a solid layer of thermal sealable material, such as separate strips of polyethylene film or other suitable thermal sealable films, are sequentially spaced on one side of a thermal sealable plastic mesh web at equal distance from one another. The pre-prepared web is used on a conventional form, fill and seal machine to form mesh bags having top and bottom fin seals with enhanced strength. The bag is primarily mesh so the product within the bag breathes easily. A thermal sealable print band may be located on the second side of the mesh. Different types of bags can be formed on different types of automatic form, fill and seal machines by modifying the specific configuration of the pre-prepared mesh web for the particular automatic form, fill and seal machine design.