We present two-dimensional simulations of finite, self-gravitating gaseous sheets. Unlike the case of infinite sheets, such configurations do not constitute equilibrium states but instead are subject to global collapse unless countered by pressure forces or rotation. The initial effect of finite geometry is to promote concentrations of material at the edges of the sheet. If the sheet is not perfectly circular, gravitational focusing results in enhanced concentrations of mass. In the second-most simple geometry, that of an elliptical outer boundary, the general result is collapse to a filamentary structure with the densest concentrations of mass at the ends of the filament. We suggest that these simple calculations have interesting implications for the gravitational evolution of overall molecular cloud structure, envisioning that such clouds might originate as roughly sheetlike sections of gas accumulated as a result of large-scale flows in the local interstellar medium. We show some examples of local clouds with overall filamentary shape and denser concentrations of mass and star clusters near the ends of the overall extended structure, suggestive of our simple ellipse collapse calculations. We suggest that cluster-forming gas is often concentrated as a result of gravity acting on irregular boundaries; this mechanism can result in very rapid infall of gas, which may be of importance to the formation of massive stars. This picture suggests that much of the supersonic ``turbulence'' observed in molecular clouds might be gravitationally generated. Our results may provide impetus for further theoretical explorations of global gravitational effects in molecular clouds and their implications for generating the substructure needed for fragmentation into stars and clusters.