Three-dimensional dilational and sinuous wave propagation on infinite or semi- infinite thin planar sheets flowing into a gas of negligible density is investigated. The assumption of thin sheets allows the reduction of the problem dimensionality by integration across the sheet thickness. For finite-amplitude disturbances, the strongest nonlinear effects occur when the cross-sectional wavenumber (l) is close to the streamwise wavenumber (k). First, dilational wave propagation is considered. When l is close to k for infinite sheets, higher harmonics are generated in the streamwise direction, and the standing wave with finite amplitude in the cross-sectional plane becomes at. As time passes, the waves return to the initial wave shape. This process is repeated in a cycle. A similar phenomenon is found in semi-infinite sheets with low Weber number. When l is close to k for semi-infinite sheets and Weber number is high, fluid accumulates into fluid lumps interspaced by one wavelength in the cross- sectional direction as well as in the streamwise direction. This leads to the formation of initially non-spherical ligaments or large droplets from the liquid sheet. Secondly, sinuous wave propagation is considered. When l is close to k for semi-infinite sheets and Weber number is high, fluid agglomerates in the edge of the sheet interspaced by half a wavelength in the cross-sectional direction as well as in the streamwise direction. A three-dimensional visualization of the computational results shows that the disturbance at the nozzle exit induces fluid to agglomerate into half-spherical lumps, which indicate the formation of ligaments or large droplets from the liquid sheet. A similar phenomenon is found in the case of infinite sheets.