The equivalent frame method (EFM) is widely used for the design of two-way reinforced concrete slab structures, and current design codes of practice permit the application of the EFM in analyzing the flat plate slab structures under gravity and lateral loads. The EFM was, however, originally developed for the flat plate structures subjected to gravity load, which is not suitable for lateral loading case. Therefore, this study, the first part of series research paper, proposed the structural analysis method for the flat plate slab structures under the combined gravity and lateral loads, which is named as the unified equivalent frame method (UEFM). In the proposed method, some portion of rotation induced in the torsional member is distributed to the flexibility of the equivalent columns, and the remaining portion is contributed to that of the equivalent slabs. In the consecutive companion paper, the proposed UEFM is verified by comparing with test results of multi-span flat plate structures. Also, a simplified nonlinear push-over analysis method is proposed, and verified by comparing to test results.