Technical Abstract: The movement of water over the soil surface under surface irrigation has been studied extensively over the last century. However, we are still faced with significant challenges in making surface irrigation systems efficient. In the past, each surface irrigation method was treated differently because of differences in the simplicity with which different phases of the irrigation could be described. This has tended to make surface irrigation analysis and design appear disjointed. In this paper, we attempt to apply the same basic procedures for the design of surface various systems, deviating where needed to make the procedures both straightforward and sufficiently accurate. The basis for these designs is the ability to predict advance, recession, the distribution of infiltrated water, and the performance for a given set of conditions. Conservation of mass is the main concept, with empirical approximations used where needed. This paper presents the relevant equations. A companion papers provides solution procedures for hand calculation and spreadsheets and discussion of how to apply these in a design setting.