The kinetics of the reactions of F atoms with hydrogen and deuterium has been studied in a discharge flow reactor combined with an electron impact ionization quadrupole mass spectrometer at nearly 2 Torr total pressure of helium and in the temperature range 220-960 K. The rate constant of the reaction F + H-2 -> HF + H (1) was determined using both relative rate method (using reaction F + Br-2 as a reference) and absolute measurements, monitoring the kinetics of F atom consumption in excess of H-2: k(1) = (1.24 +/- 0.09) x 10(-10) exp(-(507 +/- 23)/T) cm(3) molecule(-1) s(-1). The rate constant of the reaction F + D-2 -> DF + D (2) was measured under pseudo-first-order conditions in excess of D-2 over F atoms: k(2) = (8.47 +/- 0.42) x 10(-11) exp(-(670 +/- 16)/T) cm(3) molecule(-1) s(-1) (the uncertainties on both k(1) and k(2) represent precision at the 2 sigma level, the estimated total uncertainty on the rate constants being 15% at all temperatures). The kinetic isotope effect measured independently, k(1)/k(2) = (1.58 +/- 0.05) x exp((131 +/- 2)/T), was found to be in excellent agreement (within 7% in the temperature range of the work, T = 220-960 K) with the ratio of k(1) to k(2) calculated with the Arrhenius expressions for k(1) and k(2) determined in the study. The kinetic data from the present work are discussed in comparison with previous measurements and theoretical calculations.