In this study the grafting rate relation of acrylamide onto the poly (ethylene terephtha- late) fibers using benzoyl peremde was dedııced and the overall aetivation energy of grafting was calculated. The rate of grafting was found to be proportional of the 0.98 and 0.62 powers of acrylamide and benzoyl peroxide concentrations respeetively.. The overall aetivation energy was calculated to be 81.5 kj /mole in the range of 75-92°C and the overall rate constants were determined at different experimental temperatures.