In the paper we consider the problem of routing and bandwidth allocation in networks that support elastic traffic. We assume that the bandwidth demand between each source-destination (S-D) pair is specified in terms of a minimum and maximum value, and a set of flows between each S-D pair is allowed to realize these demands. (We say that a set of flows realizes the demand associated with an S-D pair, if the sum of the bandwidths allocated to these flows is greater than the minimum value assumed for the demand of that S-D pair.) In this setting, we show that routing and bandwidth allocation can be formulated as an optimization problem, where network utilization is to be maximized under capacity and the widely used maxmin fairness constraints. We describe three different algorithms to solve variants of this problem. The most important one, an efficient, original algorithm assuming multipath routing is studied in detail and illustrated with a numerical example.