A saddlebag container has a tub made of a plurality of composite fiber panels three dimensionally thermally molded or thermoformed in a chill forming process to form at least a plurality of structurally supporting tub walls and can have a lid of such construction. A preferred tub is formed of a plurality of panels with one panel three dimensionally shaped to form one sidewall and at least one of an endwall and bottom wall and another panel three dimensionally shaped to form the other sidewall that serves as a base to which the one panel is attached which can also provide a vehicle attachment mount. A preferred lid is formed of a panel that can have an outwardly extending mounting flap used to attach the lid to the base which can also serve as a hinge of the lid. A preferred tub and lid construction has at least two layers with one layer of a fibrous material and another layer of a different material that can provide a cover.