The cure kinetics of blends of epoxy resin (4,4'-tetraglycidyl diaminodiphenyl methane; TGDDM)/curing agent (diaminodiphenyl sulfone; DDS) with ATPEI-CTBN-ATPEI triblock copolymer (ABA type) were studied using differential scanning calorimetry under isothermal conditions to determine the reaction parameters such as activation energy and reaction constants. By increasing the amount of ABA in the blends, the final cure conversion was decreased. Lower values of the final cure conversions in the epoxy/ABA blends indicated that ABA hinders the cure reaction between the epoxy and the curing agent. The value of the reaction order m for the initial autocatalytic reaction was not affected by blending ABA with epoxy resin, i.e., the value was approximately 1.0. The value of n for the n-th order component in the autocatalytic analysis was increased from 2.0 to 3.4 by increasing the amount of ABA in the blends. A diffusion controlled reaction was observed as the cure conversion increased and the curing reaction was successfully analyzed by incorporating the diffusion control term in the rate equation for the epoxy/DDS/ABA blends. The glass transition temperature of the cured blend was improved from 187 to 205 degrees C and the value of the fracture toughness was also improved by about 400% compared to that of the unmodified resin at 30 wt% of ABA triblock copolymer. This is attributed to the formation of co-continuous morphology between the epoxy phase and ABA triblock copolymer phase. By increasing the amount of ABA, compressive strain, tensile stress and strain of the cured blends were increased, but the compressive stress was reduced due to the presence of CTBN rubbery phases.