Abstract Bread wheat and durum wheat genotypes were grown in field experiments at two locations in New South Wales, Australia across several years and using two sowing times (‘early’ v. ‘late’). Genotypes were grouped based on genetic similarity. Grain yield, grain size, soil characteristics and daily weather data were collected. The weather data were used to calculate water and heat stress indices for four key growth periods around flowering. Least absolute shrinkage and selection operator (LASSO) was used to predict grain yield and to identify the most influential features (a combination of index and growth period). A novel approach involving the crop water supply–demand ratio effectively summarized water relations during growth. LASSO predicted grain yield quite well (adjusted R2 from 0.57 to 0.98), especially in a set of durum genotypes. However, the addition of other important variables such as lodging score, disease incidence, weed incidence and insect damage could have improved modelling results. Growth period 2 (30 days pre-flowering up to flowering) was the most sensitive for yield loss from heat stress and water stress for most features. Although one group of bread wheat genotypes was more sensitive to water stress (drought) in period 3 (20 days pre-flowering to 10 days post-flowering). Evapotranspiration was a significant positive feature but only in the vegetative phase (pre-flowering, period 1). This study confirms the usefulness of LASSO modelling as a technique to make predictions that could be used to identify genotypes that are suitable candidates for further investigation by breeders for their stress-tolerance ability.