We develop a transfer matrix model that can accurately predict scattering properties of light and surface plasmons by structures consisting of multiple grooves in a metal film. To this end, we first explore the basic scattering processes at a single groove, and use this understanding to build a multigroove model. The scattering properties of N-groove structures for incident surface plasmons of unit amplitude can be predicted with an absolute error of 0.01N in only milliseconds on a dual-core 2.33-GHz processor, which is orders of magnitude faster than full-field electromagnetic simulations. The ability to quickly calculate light scattering properties of multigroove structures will enable rapid optimization of the next generation of aperiodic plasmonic devices.