An important problem in multifiber WDM networks is to decide how many fibers per link are required to guarantee high network performance. The fiber requirement may depend on many factors, e.g., the network topology, traffic patterns, the number of wavelengths per fiber, and the routing algorithm employed in the network. We study the fiber requirement under dynamic traffic in different topologies with alternate path routing (APR) in this paper. A new analytical model is developed to evaluate the blocking performance of such networks. Our analytical and simulation results show that the number of required fibers per link to provide high network performance is slightly higher in the APR than the fixed-path routing (FPR). However, a small number of fibers per link are still sufficient to guarantee high network performance in both the regular mesh-torus networks and the irregular NSFnet with APR. Since multiple fibers have the same effect as limited wavelength conversion, our analytical model is also applicable in networks with limited wavelength conversion.