This investigation developed statistical models to estimate one repetition maximum (1 RM) muscular strength using submaximal ratings of perceived exertion (RPE) as predictor variables. Ten- to 14-year-old girls (n = 35) and boys (n = 35) performed two sets (10 repetitions) of biceps curl (BC) and knee extension (KE) exercise using weights approximating 30% and 50% 1 RM. RPE was assessed during the final repetition of each set using the children's OMNI Resistance Exercise Scale (0-10). Sex-specific statistical models predicted 1 RM using RPE derived from both sets of BC and KE exercises. For both girls and boys, RPE ranged from 3.7 to 6.6 for BC and 4.1 to 7.2 for KE. Group mean 1 RM was (a) girls: BC, 7.44 kg, KE, 13.25 kg and (b) boys: BC, 9.19 kg, KE, 16.24 kg. One repetition maximum prediction models for girls were significant (P < 0.01) for BC (r = 0.87) and KE (r = 0.89). One repetition maximum prediction models for boys were significant (P < 0.01) for BC (r = 0.89) and KE (r = 0.87). The RPE predictors were practical and accurate measures, making the 1 RM models potentially applicable when assessing large numbers of children in short time periods.