Plants constantly fight with stressful factors as high or low temperature, drought, soil salinity and flooding. Plants have evolved a set of stress response mechanisms, which involve physiological and biochemical changes that result in adaptive or morphological changes. At a molecular level, stress response in plants is performed by genetic networks, which also undergo changes in the process of evolution. The study of the network structure and evolution may highlight mechanisms of plants adaptation to adverse conditions, as well as their response to stresses and help in discovery and functional characterization of the stress-related genes. We performed an analysis of Arabidopsis thaliana genes associated with several types of abiotic stresses (heat, cold, water-related, light, osmotic, salt, and oxidative) at the network level using a phylostratigraphic approach. Our results show that a substantial fraction of genes associated with various types of abiotic stress is of ancient origin and evolves under strong purifying selection. The interaction networks of genes associated with stress response have a modular structure with a regulatory component being one of the largest for five of seven stress types. We demonstrated a positive relationship between the number of interactions of gene in the stress gene network and its age. Moreover, genes of the same age tend to be connected in stress gene networks. We also demonstrated that old stress-related genes usually participate in the response for various types of stress and are involved in numerous biological processes unrelated to stress. Our results demonstrate that the stress response genes represent the ancient and one of the fundamental molecular systems in plants.