The main aim of the "System for Analyzing Mathematical Flow Models" (FMA system) described in this paper is to supply the decision-maker with a computerized tool for quantitative investigation of problem that can be described, at least partially, in terms of standard mathematical models of the Bow type. The FMA system permits the decision-maker to find states of the considered model that satisfy all introduced constraints, are close to the desirable structure, and are optimal with respect to single- or multiobjective evaluation.