With vast regions already experiencing water shortages, it is becoming imperative to manage sustainably the available water resources. As agriculture is by far the most important user of freshwater and the role of irrigation is projected to increase in face of climate change and increased food requirements, it is particularly important to develop simple, widely applicable models of irrigation water needs for short- and long-term water resource management. Such models should synthetically provide the key irrigation quantities (volumes, frequencies, etc.) for different irrigation schemes as a function of the main soil, crop, and climatic features, including rainfall unpredictability. Here we consider often-employed irrigation methods (e.g., surface and sprinkler irrigation systems, as well as modern micro-irrigation techniques) and describe them under a unified conceptual and theoretical framework, which includes rainfed agriculture and stress-avoidance irrigation as extreme cases. We obtain mostly analytical solutions for the stochastic steady state of soil moisture probability density function with random rainfall timing and amount, and compute water requirements as a function of climate, crop, and soil parameters. These results provide the necessary starting point for a full assessment of irrigation strategies, with reference to sustainability, productivity, and profitability, developed in a companion paper [Vico G, Porporato A. From rainfed agriculture to stress-avoidance irrigation: II. Sustainability, crop yield, and net profit. Adv Water Resour 2011;34(2):272-81]. (C) 2010 Elsevier Ltd. All rights reserved.