A mathematical programming method for the analysis of the cable-stayed bridge with unilateral supports is presented. A detailed comparative study of the nonlinear phenomenon arising from the unilateral restriction at intermediate piers of the bridge is carried out. The characteristics of the unilateral supports can be described by a set of control variables which are of multi-folded constitutive relations with piecewise linearity. By using the parametric variational principle, it leads to the solution of a quadratic programming problem or to a linear complementary problem. The distinguished figures of the cable-stayed bridge with this kind of support are illustrated' by numerical examples.