Three-dimensional coupled-wave theory is extended to model triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization. A generalized coupled-wave equation is derived to describe the sixfold symmetry of the eigenmodes in a triangular lattice. The extended theory includes the effects of both surface radiation and in-plane losses in a finite-size laser structure. Modal properties of interest including the band structure, radiation constant, threshold gain, field intensity profile, and far-field pattern (FFP) are calculated. The calculated band structure and FFP, as well as the predicted lasing mode, agree well with experimental observations. The effect of air-hole size on mode selection is also studied and confirmed by experiment.