The sorption kinetics of Pb²⁺ and Cu²⁺ ions in aqueous solution by unmodified and mercaptoacetic acid modified biomass of Nypa fruticans shoot has been investigated. The equilibrium sorption capacity of Pb²⁺ and Cu²⁺ was determined from the Langmuir equation and found to be 15.59 mg/g and 21.85 mg/g for unmodified biomass and 52.86 mg/g and 66.71 mg/g for modified biomass at 30ºC. The time dependent studies showed relatively rapid sorption of 5 - 10 min to reach equilibrium for both metal ions. A batch sorption model, based on the assumption of the pseudo-second-order mechanism, was applied to predict the rate constants (g mg^-1 min^-1), which were found to be 3.59 x 10^-4 (Pb²⁺) and 1.85 x 10^-4 (Cu²⁺) and 2.82 x 10^-2 (Pb²⁺) and 3.67 x 10^-2 (Cu²⁺) on unmodified and mercaptoacetic acid modified biomass respectively. The activation energy of the sorption of Pb²⁺ and Cu²⁺ on Nypah palm reveals an endothermic process.