Energetic neutrons, produced as protons interact with matter, dominate the radiation shielding environment for proton accelerators. Because of the scarcity of data describing the shielding required to protect personnel from these neutrons, absorbed dose and dose-equivalent values are measured as a function of depth in a thick concrete shield at neutron emission angles of 0, 22, 45, and 90 deg for 230-MeV protons incident upon stopping-length aluminum, iron, and lead targets. Neutron attenuation lengths vary sharply with angle but are independent of the target material. Comparing results with prior shielding calculations, the High-Energy Transport Code overestimates neutron production and attenuation lengths in the forward direction. Analytical methods compare favorably in the forward direction but overestimate the production and attenuation lengths at large angles. The results presented are useful for determining the shielding requirements for proton radiotherapy facilities and as a benchmark for future calculations.