An investigation has been made for understanding the transport behaviour of organic solvents through linear low-density polyethylene (LLDPE)/ethylene vinyl acetate (EVA) blend membranes with special reference to the effects of blend ratio, concentration of cross-linking agent, penetrant size and temperature. Attempts have been made to relate the transport parameter with the morphology of the blend. The various transport parameters such as diffusion coefficient (D), permeation coefficient (P) and sorption coefficients (S) were evaluated at different diffusion conditions. The results were compared with theoretical predictions and found that the diffusion process follows anomolous type behaviour. The blends show dispersed/matrix and co-continuous phase morphologies depending on the composition. Dynamic vulcanization leads to fine and uniform distribution of the dispersed domains with a stable morphology. Among the blends E-70 sample shows the maximum solvent uptake and E-30 the minimum. The solvent uptake of blend varies with concentration of cross-linking agent. Molecular size of the solvent is a decisive factor in the solvent uptake. The rate of sorption and maximum solvent uptake increase with increase of temperature. Irrespective of the solvents used, the maximum solvent uptake increases with increase of temperature. The observed sorptivity, diffusivity and permeability are associated with cross-link densities of different samples. The D, S and P values increase with increase of EVA content in the blend.