The radioactive concentrations of (18)F, (88)Y and (152)Eu solutions and the activity of (222)Rn gas ampoules are measured using a primary method involving 4pigamma NaI(Tl) integral counting with a well-type NaI(Tl) detector and efficiencies computed by Monte Carlo simulations. The simulations use the GEANT code coupled with a routine (sch2for), which generates randomly the decay paths and emissions depending on the decay scheme parameters. The resulting radioactive concentrations of (88)Y, (152)Eu and (18)F are found to agree with those measured with other primary measurement methods, such as 4pi (beta, e, X)-gamma coincidence counting or liquid scintillation counting. Results of the determination of the activity of (222)Rn gas ampoules by this method also match the results of an absolute standardisation technique in which radon is condensed onto a cold surface and its alpha-emissions are detected through an accurately specified solid angle.