In this two-part paper, the optimization of the electromechanical coupling coefficient for thin-film piezoelectric devices is investigated both analytically and experimentally. The electromechanical coupling coefficient is crucial to the performance of piezoelectric energy conversion devices. A membrane-type geometry is chosen for the study. In part I a one-dimensional model is developed for a membrane composed of two layers, a passive elastic material and a piezoelectric material. The lumped-parameter model is then used to explore the effect of design and process parameters, such as residual stress, substrate thickness, piezoelectric thickness and electrode coverage, on the electromechanical coupling coefficient. The model shows that the residual stress has the most substantial effect on the electromechanical coupling coefficient. For a given substrate material and thickness an optimum piezoelectric thickness can be found to achieve the maximum coupling coefficient. The substrate stiffness affects the magnitude of the maximum coupling coefficient that can be obtained. Electrode coverage was found to be important to electromechanical coupling. The model predicts an optimum electrode coverage of 42% of the membrane area. The model developed in part I formed the basis for the parameters studied experimentally in part II.