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Water resources all over the world are facing several problems such as scarcity, pollution, climate change, and global warming. Arid zones especially suffer from either severe drought or severe floods. Scientific analysis of flood events is difficult because of lacking flood measurement data and rainfall-runoff models that are suited for arid regions. Researchers in the field of hydrology are developing rainfall-runoff models for storm runoff predictions since 1932. However, it is noticeable that most research papers, books, and theses are considering studies in temperate regions, while arid zones are lacking such studies. The main objective of this paper is to derive a mathematical model called Ari-Zo, using regression analysis, to predict flood peaks, time to peak, and time of concentration from rainfall storms in arid zones. The data used in this study relied on storm measurements registered at Allith and Yiba basins and their subcatchments (eight subbasins) located in the southwestern part of Saudi Arabia. The stream flow data method has been used to derive the unit hydrograph in the Ari-Zo model from 36 storms. The study developed several mathematical relationships between the hydrological variables and the regional topography of the basins. The mathematical equations obtained from this study are the discharge peaking factor, time of concentration, and time to peak. The Ari-Zo model results are compared with the results of the National Resources Conservation Service (NRCS) method and showed substantial differences. The peaking factors of NRCS range between 0.0646 and 0.2582, while in Ari-Zo, it ranges between 0.0513 (low flood case) and 1.9465 (very extreme flood case). The ratio between the time to peak and the time of concentration in NRCS is equal to 0.667, while in Ari-Zo, it ranges between 0.05 and 0.5 and on average, it is 0.276. The parameters of time of concentration in Ari-Zo model are different from those of Kirpich equation. The study recommends using the Ari-Zo model for arid zone hydrological studies.