Extensive neutron and gamma attenuation measurements have been performed in magnetite and ordinary concrete up to a depth of 2 m to collect reference data for a study of the accuracy attainable by shield calculation methods. Experimental facilities and the configurations studied are described accurately enough to enable the reader to test his own methods against these measurements. Great weight has been laid upon absolute accuracy and a thorough error analysis. The fluxes measured are compared to those calculated by an earlier version of the British 18-group removal method (RASH B3), by an improved removal method (NRN) developed atAB Atomenergi, and by numerical integration of Boltzmann equation (NIOBE). Calculations with the newer methods give fluxes that are generally within a factor of 2 of the true values. Any greater accuracy seems to be difficult to obtain in practice in spite of possible improvements in the mathematical solution of the transport problem. The greatest errors originate in going from the true geometry to that used for calculation, in the uncertainty of material properties in the case of concrete, and in approximations and inaccuracies of radiation sources.