Laser-ablated beryllium atoms react with H-2 upon co-condensation in excess hydrogen and neon to form BeH2 and (BeH2)(2), which are identified through isotopic substitution and DFT calculations. Unreacted Be atoms isolated in solid neon or hydrogen are excited to the P-1(0) state and react further with H-2 to enhance the BeH2 and (BeH2)(2) concentrations and produce (BeH2)(n) polymers, The series of strong infrared-active parallel Be-H-Be bridge-bond stretching modes observed for (BeH2)(n) polymers suggests one-dimensional structures, and this conclusion is supported by DFT calculations. The computed polymerization energy per BeH2 unit is about 33 kcal/mol.