A classical solution technique is developed for analyzing multi-girder composite bridge structures. A set of biharmonic equations is employed to solve a set of differential equations for plane stress and flexural displacements for each deck slab between girders. Boundary conditions are obtained at girder-slab junctions and at free edges by considering the equilibrium and compatibility conditions on the slab-girder interface and at the interface of two neighbouring deck-slabs. Simultaneous solutions can be obtained for different geometrical arrangements of multi-girder composite structures, by substituting the corresponding derivatives of the solutions into the boundary conditions. The validity of the solutions is verified by comparison with experimental results and with results of a finite element analysis. Using the solutions developed in this paper, the behavior of multi-girder composite bridges can be examined efficiently by varying the controlling variables and conducting an extensive parametric study.