The authors presented a proportioning method for member sections of single layer reticulated domes in the previous papers based on a second-order elastic analysis. In the first part of the present paper, a method complementary to the above method is proposed based on linear buckling stress obtained from linear buckling analysis, being more familiar than the second-order elastic analysis. The proportioning method based on linear buckling stress is verified through elasto-plastic simulation for roller supported single layer reticulated dome. The second part of the present paper discusses buckling stresses and buckling loads of single layer reticulated domes under non-uniform loadings. The usefulness of this proportioning method under non-uniform loadings is discussed and verified through elasto-plastic simulation for roller supported single layer reticulated domes.