Cowpea, Vigna unguiculata (L) also known as southern peas is a yearly grown legume that is native from Africa but now are widely cultivated around the world, particularly in South-east Asia, Latin America, and Southern United States. Moreover, the crop can endure excessive heat but is also susceptible to frost. Cowpea are profitable for the agricultural industry and are often utilized as a supplement nutrition for both human and animals. As a result, it serves as a significant low-cost source of premium plant protein across many poor households. Moreover, the crop is widely used as a green mature and as a cover crop. Furthermore, the cowpea thrives in a wide range of soil types and soil conditions. The crop's capacity to withstand drought is a special trait for coping with the severe environmental challenges caused by global warming. However, due to a prolonged lack of rain during the rainy season, South African agriculture is subject to severe edaphic and climatic challenges, including water stress and insufficient soil nutrients. Consequently, this work focuses on analyzing cowpea's growth phases by proposing novel regression models under the impact of water stress for local farmers to optimally map out cultivation over the period of drought without imperiling their yields. The proposed regression models predict the cowpea's growth at various periods of water stress including vegetative to maturity, flower to maturity and excellent water through the season. At each period of water stress, regression models of the leaf area and shoot dry weight are developed. The various growth phases of the cowpeas were studied under three-pot test conditions. The results suggest that water stress at initial growth phases decreased the shoot dry weight (SDW), and leaf area (LA) of studied cowpeas. Growth analysis of cowpeas species cultivated in pure stands for the distinctive periods showed that the leaf area was the most explanatory variable in the SDW of cowpea at the initial growth phase. The correlation coefficient of the LA and SDW of cowpeas produced by the proposed models at vegetative to maturity, flower to maturity and excellent water through the season are 0.957 and 0.983, 0.963 and 0.980, 0.957 and 0.976