A modular bag system has components for constructing a carrying bag of a variable, customized shape. The bag includes a main body and side gusset panels. The main body has edges provided with zippers. Two lateral edges are approximated to form a tube; at least part of the outer edge of each side gusset panel has a zipper for joining to the ends of the tube. The bag may also include a handle piece provided with a zipper for joining to the main body. The side gusset panels each have a round shape, a substantially square shape, an oblong shape, or a trapezoidal shape, for forming a duffel/gym bag, an overnight/weekender bag, a briefcase/portfolio, or a tote bag, respectively.