In order to prevent unstable operation, or "chatter", of a pressure relief the API guidelines recommend limiting the irreversible pressure loss in the inlet line to a pressure relief valve to no more than 3% of the valve set pressure. This criterion is based on steady-state operating conditions and a typical blow-down pressure for the valve of about 7% of the set pressure. However, the stability of the valve is also influenced by other factors such as the dynamic response of the valve disk to the unsteady pressures and forces exerted by the fluid on the disk. A model for the opening lift dynamic response of a pressure relief valve in gas/vapor service is presented here which accounts for all of these effects through a set of five coupled nonlinear algebraic/differential equations. These equations are solved by a numerical method that can be implemented on a spreadsheet to predict the position of the valve disk as a function of time for given valve characteristics, operating conditions, and installation parameters. The model incorporates the influence of the various parameters on the stable/unstable nature of the disk response. An example is presented for a typical valve that illustrates the various modes of stable and unstable dynamic response that can be predicted by the model under various conditions. Two additional papers will be forthcoming: Part II - Experimental Investigation and Part III - Analysis of Data and Comparison with Model Predictions. (C) 2013 Elsevier Ltd. All rights reserved.