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The study of the impact of high temperature and drought on the yield of major staple crops can provide important scientific support for the decision-making of agricultural sustainable development. Based on the temperature and precipitation data of the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA 5 for northern China, this paper calculates three indexes, the standard precipitation index (SPI), standardized precipitation evapotranspiration index (SPEI) and the extreme degree-day (EDD), from 1979 to 2017. Monthly SPI and monthly SPEI were calculated at 1 – to – 12 month lags, and EDD was calculated per crop growth season. The yield of winter wheat, spring wheat and summer maize in each province of the study area from 1979 to 2017 was de-trended, and the relative fluctuation of the yield of the three crops was calculated. The change trends of SPI, SPEI and EDD were analysed using the Mann–Kendall test and Sen's slope. The single and interactive effects of high temperature and drought on crop yield were studied using multidimensional Copula function. The results show that: 1) Both high temperature and drought stress in northern China show an increasing trend. The drought trend in the study area detected based on SPEI was greater than the drought trend detected by SPI. The difference between SPEI and SPI in the winter wheat growing season was smaller than that in the spring wheat and maize growing seasons. 2) With the increase in EDD and the decrease of SPI/SPEI values, the probability of negative yield fluctuation gradually increased, and the probability of positive yield fluctuation gradually decreased. Under the same drought and high temperature conditions, the probability of yield fluctuation varies among different crops and different provinces. Drought has a greater impact on crop yield than high temperature. Both the single and interactive effects of drought and high temperature on yield are nonlinear. 3) Irrigation can effectively alleviate the impact of drought and high temperature on yield. In heavily irrigated provinces, the effects of both high temperature and drought on crop yield are not obvious. • The impact of high temperature and drought stress on yield is analysed by a probability model. • The effects of high temperature and drought on yield are non-linear. • Irrigation can offset some of the effects of high temperature and drought on yield. • SPEI may overestimate the impact of drought on yield while SPI may underestimate. [ABSTRACT FROM AUTHOR]