Gamma-ray dose rates on the exterior surfaces of cylindrical vessels containing radioactive solutions are calculated using a model based on the distributed point source approximation. A cylinder is subdivided into a number of annular sector segments of equal volume and the dose rate from each segment is combined to give the total dose rate at a point on the exterior surface of the cylindrical container. Calculated results for the method are compared with experimentally determined results for (a pure -emitter) and (a mixed and -emitter) in acrylic containers of various wall thicknesses, as well as for single containers made from polycarbonate and polypropylene; good agreement was obtained. Calculated results for the -ray dose rates to the skin of the fingers, for partially filled plastic syringes, are compared with other published results, for , , , , and in syringes of various diameters and wall thicknesses; good agreement was obtained. The calculations are extended to provide results for the -ray dose rate distribution along the external surfaces of partially filled syringes for and . These results are used to objectively derive guidelines for the safe handling of cylindrical vessels containing -emitting radionuclides, without the use of extra shielding. It was found that the weekly dose limit to the skin, of 10 mSv, is exceeded if the fingers are in contact with the container, over the active volume, for periods greater than about one minute. However, if handled at the rear of the syringe barrel a typical weekly work load can be managed without exceeding dose limits. It is recommended, when using syringes without syringe guards, that the fingers should never approach the active volume closer than the rear end of the syringe barrel, and that syringes should not be filled beyond 75% of their capacity.