This work, in two parts, proposes a theoretical formulation (Part 1) and its finite element implementation (Part 2) for an adaptive sandwich shell of revolution that uses the transverse shear response of a piezoelectric core sandwiched between two elastic faces. For this, the former is assumed initially poled along the meridian but subjected to electric potentials on its fully electroded inner and outer surfaces. The model assumes the first-order shear deformation theory for each layer and enforces the displacement continuity conditions at the core to faces interfaces. Besides, the sandwich theory retains the shell transverse deflection together with the mean and relative tangential displacements and bending rotations of the elastic faces as mechanical independent variables. These are augmented by the electric potential in the piezoelectric core, in order to effectively consider the electromechanical coupling. Implementation and validation of the theoretical formulation developed in this part are presented in Part 2 of the paper.