A systematic investigation of the sound radiation of orthogonally stiffened plates is presented using a numerical procedure that combines the finite element method with the Rayleigh integral. Results are computed for plates with different numbers of stiffeners, stiffener depth, and plate thickness to investigate the dependence on the most important parameters. Differences are seen in the radiation efficiency of stiffened plates compared with unstiffened panels. In the monopole region, the result depends on the type of mode that dominates the response. For excitation within a bay, the radiation efficiency is reduced to that of a single bay if the stiffeners are stiff enough. If excited on a stiffener, the plate tends to radiate sound over its full surface area. In the short-circuiting region, on average, the radiation efficiency is equal to that of a smaller bay-sized panel with clamped edges, regardless of the excitation position. Results from the systematic study of 120 numerical cases are used to develop asymptotic formulae for the radiation efficiency of stiffened plates based on existing formulae for unstiffened panels. For all tested configurations, the average difference between the formulae and the numerical calculations was 0.3 dB over the whole frequency spectrum, with a standard deviation of ±1.5 dB. Between the frequency bands, the mean value varied between −2 and 3 dB, with a standard deviation of up to ±1.5 dB in the monopole region and a larger variation of up to ±5 dB in the short-circuiting region.