We previously observed a rapid increase in the incidence of renal cell carcinoma (RCC) in men and women between 1935 and 1989 in the USA, using data from the Connecticut Tumor Registry. This increase appeared to be largely explained by a positive cohort effect, but no population-based study has been conducted to comprehensively examine age-period-cohort effects by histologic types for the past decade. We calculated age-adjusted and age-specific incidence rates of the two major kidney-cancer subtypes RCC and renal urothelial carcinoma, and conducted an age-period-cohort analysis of 114 138 incident cases of kidney cancer reported between 1992 and 2014 to the Surveillance, Epidemiology, and End Results programme. The age-adjusted incidence rates of RCC have been increasing consistently in the USA among both men and women (from 12.18/100 000 in 1992-1994 to 18.35/100 000 in 2010-2014 among men; from 5.77/100 000 in 1992-1994 to 8.63/100 000 in 2010-2014 among women). Incidence rates generally increased in successive birth cohorts, with a continuing increase in rates among the younger age groups (ages 0-54 years) in both men and women and among both Whites and Blacks. These observations were confirmed by age-period-cohort modelling, which suggested an increasing birth-cohort trend for RCC beginning with 1955 birth cohorts, regardless of the assumed value for the period effect for both men and women and for Whites and Blacks. Known risk factors for kidney cancer may not fully account for the observed increasing rates or the birth-cohort pattern for RCC, prompting the need for additional etiologic hypotheses (such as environmental exposures) to investigate these descriptive patterns. © The Author(s) 2019; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association.