A theoretical study is conducted for the lateral torsional buckling of wooden beam-deck assemblies consisting of twin beams braced by tongue-and-groove decking at the top. Two models are developed, each with a series of analytical and numerical solutions formulated. The first model targets twin-beam-deck assemblies where deck boards and other components are detailed to provide full continuous lateral restraint while the second model is built for situations where the beams are allowed to sway laterally and the relative lateral movement between the beams is partially restrained by the deck boards. In the first model, focus is on wind uplift while in the second model, both gravity and uplift loading scenarios are investigated. In the first model, an energy method is adopted and the principle of stationary potential energy is evoked to formulate closed-form solutions, energy-based solutions and a finite element solution. The validity of the present solutions is verified against a finite element based ABAQUS model. Similarly, a family of solutions is developed under the sway model and verified against the ABAQUS. Parametric studies are conducted for both models to examine the effects of various variables on the buckling capacity. A comparative investigation on the behavioral difference between the two models under ABAQUS is also presented. Overall, the restraining effects of deck boards bracing either on the beam compression or tension side is observed to have a significant influence on the lateral torsional buckling capacity of the twin-beam-deck assemblies.