Los Alamos National Laboratory is building room-temperature rf accelerating structures for the Spallation Neutron Source (SNS). These structures, for H(sup (minus)) ions, 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(beta)(lambda) FFODDO lattice with every third drift tube available for diagnostics and steering. The CCL uses a 13(beta)(lambda) FODO electromagnetic quadrupole lattice. Diagnostics and magnets occupy the 2.5(beta)(lambda) spaces between 8-cavity segments. This paper discusses design of the rf cavities and low-power modeling work.