Los Alamos National Laboratory is building room-temperature rf accelerating structures for the Spallation Neutron Source (SNS). These structures, for H/sup i/ons, consist of six 402.5 MHz, 2 MW drift-tube linac (DTL) tanks from 2.5 to 87 MeV followed by four 805 MHz, 4 MW coupled-cavity linac (CCL) modules to 186 MeV. The DTL uses permanent magnet quadrupoles inside the drift tubes arranged in a 6/spl beta//spl lambda/ FFODDO lattice with every third drift tube available for diagnostics and steering. The CCL uses a 13/spl beta//spl lambda/ FODO electromagnetic quadrupole lattice. Diagnostics and magnets occupy the 2.5/spl beta//spl lambda/ spaces between 8-cavity segments. This paper discusses design of the RF cavities and low-power modeling work.