The impact of the genotype‐specific leaf morphological and anatomical characteristics on the ability of wheat plants to preserve leaf water balance and cell membranes stability under drought stress was investigated. Seedlings of six modern semi‐dwarf (carriers of Rht, Reduced height genes) and six old tall bread wheat varieties were subjected to soil drought by withholding watering for 6 days. Morpho‐anatomical traits (leaf area, perimeter, thickness, stomata and trichome density) of daily watered (control) plants were characterized by light microscopy, scanning and image analyses. The leaf water status in both control and stressed plants was determined by measuring the relative water content (RWC). The leaf cell membranes stability in stressed plants was estimated by conductometric determination of the membranes injury index. On average, the modern semi‐dwarf varieties had less leaf area and leaf perimeter, and less dissection index, a parameter characterizing the leaf shape. Under drought stress, the modern genotypes maintained better water balance evidenced by significantly higher leaf RWC and better‐preserved the cell membranes stability supported by significantly lower Injury index. The correlations between morpho‐anatomical traits in control plants and drought tolerance‐related traits showed that the higher the leaf dissection index (i.e. more oblong leaves), the greater the water loss and the leaf membrane damages after desiccation were. The effect of shape of the evaporating surface on the water loss was modelled using wet filter paper. Similar to plant leaves, the evaporation and, respectively, water loss from paper pieces of more oblong shape (i.e. higher dissection index) was more intensive. The elucidation of the impact of the leaf shape on transpiration might contribute to better understanding of the mechanisms used by plants to maintain water reserves during drought stress and could be a basis for developing of simple and fast screening methods aiding the selection of drought tolerant genotypes.