To expand the torrential rain which is a meso-and-micro scale weather process to a meso-and-long scale weather process, in this paper we choose the middle and lower reaches of the Yangtze River (MLRYZ) as a sample region, and propose the conception of "Cumulative Effect" of torrential rain (CETR) by using the daily precipitation observational data from 740 stations in China. On the statistical analysis of observations, we define CETR as the cumulation or superposition of many torrential rain processes, and three indexes, which are continuous time (Ld), control area (Ar) and precipitation contribution rate (Qs), which are used for explaining the conception of CETR. Then taking these three indexes into consideration, we establish the intensity index of CETR (BQDI) and study the relationship between the BQDI and the summer precipitation in MLRYZ. Results show that the interannual and interdecadal variations of BQDI are similar to those of summer precipitation in MLRYZ. The distribution of correlation coefficient between the BQDI and the summer precipitation in Eastern China and the composite analysis of representative years in BQDI show a large positive relation area in MLRYZ (significance test at the 95% level) and two large negative relation areas in North and South China (significance test at the 95% level), which reveals that the variations of BQDI not only correspond to the variations of summer precipitation in MLRYZ but also correlate with the distribution of summer precipitation in Eastern China to some extent. Besides, an empirical orthogonal analysis is performed on the frequency of torrential rain in MLRYZ, we find that the four major spatial modes of torrential rain are also similar to those of summer precipitation in MLRYZ. In conclusion, the precipitation caused by CETR greatly influences even determines the amount and distribution of summer rainfall, which is worth further investigating.