An analysis of surface-emitting terahertz quantum-cascade lasers operating at wavelengths near 100 μm is presented. The devices use distributed feedback through second-order Bragg metal gratings to generate strong emission of radiation normal to the laser surface. The analysis is based on coupling between the exact Floquet-Bloch eigenmodes of infinite periodic structures in finite length devices. The results show performance of surface-emitting terahertz lasers comparable to edge-emitting devices, with high radiative efficiencies and low threshold gains. Using phase-shifts in the grating, high-quality single-lobe beams in the farfield are obtained.