Identification and screening of grasses with excellent drought tolerance is a desirable strategy in breeding drought-tolerant turf and forage cultivars. Not all fescue selections and cultivars may be equally drought tolerant. An Atlas fescue (Festuca mairei St. Yves) selection and three tall fescue (Festuca arundinacea Schreb.) cultivars—Barolex, Kentucky 31, and Falcon II—were subjected to increasing drought stress for a 12-week period. Soil water content (SWC), leaf elongation (LE), leaf water content (LWC), and leaf water potential (Ψw) were measured weekly, and root length (RL) and biomass (RM) were recorded after 12 weeks. The SWC declined progressively during the 12-week drought treatment for all grasses. However, for the three tall fescue cultivars, the SWC decreased at a faster rate than for Atlas fescue. This indicated that Atlas fescue extracted soil water more slowly and developed less-intensive stress than the three tall fescue cultivars. The LE, LWC, and leaf Ψw decreased in drought-treated plants of all grasses; nevertheless, the values for the Atlas fescue remained similar to control plants for a longer period of time than the values for the three tall fescue cultivars. Drought stress significantly reduced root biomass and root length of the grasses. These four Festucas avoid drought stress through changes in leaf and root morphology and probably through osmotic adjustment to maintain sufficient turgor pressure in the growing zone for leaf elongation. The slower decrease in LE, LWC, and leaf Ψw for Atlas fescue during the drought-stress period suggested greater drought tolerance and the potential value for improving this character in a breeding program.