We present a methodology for modeling atomically layered nanoporous carbonaceous solids. Our method models carbon atoms interacting on sets of analytically defined surfaces, in conjunction with reverse Monte Carlo techniques (RMC). Our approach allows the construction of large, physically realistic nanoporous models of low-density carbonaceous solids that are both physical and statistically consistent with experimental observations. To demonstrate the flexibility of our approach and to investigate different mesostructures, we have modeled two nanoporous structures of glassy carbon. One model is comprised of multiple surfaces with the same center of symmetry, and the other is based on sets of parallel surfaces. The resulting models contain highly curved graphitic regions that also resemble the glassy carbon microstructure observed in high-resolution electron microscopy.