Abstract The elastic optical networks, a.k.a., flexgrid networks, have flexible spectrum allocation. Such flexibility is possible due to the division of the spectrum into narrow frequency slots and the use of bandwidth-variable transponders. This enables the demand, in terms of band request, to be contiguously allocated starting from any available slot of the spectrum. In this context, the RSA (Routing and Spectrum Allocation) was proposed as an offline optimization problem of allocating the optical transmission resources in order to meet a predefined set of demands. This work deals with the capacitated version of the RSA problem. To solve it, we develop a multi-commodity flow formulation based on ILP (Integer Linear Programming) and a load balancing procedure that generate promising paths for an ILP formulation from the literature. Extensive computational experiments show that the proposed solution approaches are capable of obtaining high quality solutions on a variety of scenarios.