In any structural design, safety and economy of the structures are the main objectives therefore, it is necessary to obtain the optimum geometric shape of the structure so that it can carry the imposed load safely and economically. In the present paper, analysis and optimization of the rectangular box girder bridges subjected to IRC loading are presented. The shape optimization of the box girder bridge with volume minimization as the objective are subjected to a constraint on Von-Mises stresses. Numerical examples of single and twin cell box girder sections are considered for analysis and optimization. Ansys 13.0 is used for analysis and optimization. For the single cell box girder bridge, the volume of the structure was reduced by 40 percent and 54 percent volume reduction was obtained for the twin cell box girder.