The distribution of amyloid beta peptide 42 (Aβ42) between model exosomal membranes and a buffer solution was measured. The model membranes contained liquid-ordered regions or phosphatidylserine. Results demonstrated that up to ca. 20% of amyloid peptide, generated in the plasma (or intracellular) membrane as a result of proteolytic cleavage of amyloid precursor proteins by β- and γ-secretases, can stay within the membrane milieu. The selection of RNA aptamers that bind to Aβ42 incorporated into phosphatidylserine-containing liposomal membranes was performed using the selection-amplification (SELEX) method. After eight selection cycles, the pool of RNA aptamers was isolated and its binding to Aβ42-containing membranes was demonstrated using the gel filtration method. Since membranes can act as a catalytic surface for Aβ42 aggregation, these RNA aptamers may inhibit the formation of toxic amyloid aggregates that can permeabilize cellular membranes or disrupt membrane receptors. Strategies are proposed for using functional exosomes, loaded with RNA aptamers specific to membrane Aβ42, to reduce the oxidative stress in Alzheimer’s disease and Down’s syndrome.