All-silica zeolite frameworks doped with methylene and amine groups are studied using density functional theory-based electron structure calculations. Strain energies are calculated in a novel way, by comparing zeolite energies with appropriate polymer reference systems. The modified zeolites are found to be mechanically stable structures with surprisingly little strain. Distortions due to impurities result in broadened Si-O-Si angle distributions in the lattice surrounding defects. Our results suggest that zeolites can accommodate both methylene and amine groups at high concentrations with minimal strain. The amine-doped zeolites are strong Lewis bases suggesting novel applications in base catalysis.