Based on our recently developed Fourier Monte Carlo algorithm [A. Tröster, Phys. Rev. B 76, 012402 (2007)] we propose a novel approach to study the elasticity of solid and hexatic membranes. In detail, we offer three different but related approaches to study the low-temperature ``flat'' phase, based on (i) Wilson's momentum shell renormalization group scheme for finite shell thickness, (ii) a computational version of field-theoretic renormalization methods, and (iii) a direct evaluation of the correlation function of the membrane's Fourier-transformed unit normals in Fourier space using a small wave vector cutoff. These calculations are expected to be highly relevant for understanding the important problem of the formation of intrinsic ripples in graphene sheets. Moreover, our pioneer approaches (i) and (ii) should also be extremely interesting from a theoretical point of view, as they both constitute exciting new nonperturbative computational renormalization group schemes.