Throughput scaling law of a large wireless network equipping directional antennas at each node is analyzed based on the information-theoretic approach. More specifically, this paper considers a general framework in which the beamwidth of each node can scale at an arbitrary rate relative to the number of nodes in the network. We introduce an elastic routing protocol, which enables to increase per-hop distance elastically according to the beamwidth, while maintaining an average signal-to-interference-and-noise ratio at each receiver as a constant. This elastic routing is shown to achieve a much better throughput scaling law than that of the conventional nearest-neighbor multihop routing. The gain comes from the fact that more source-destination pairs can be activated simultaneously as the beamwidth becomes narrower, which eventually leads to a linear throughput scaling law.