A model of two-layer cylindrical interstellar dust grains is used to calculate the interstellar extinction curves in the visible and near infrared regions of the spectrum and the ratio R /sub V/ of the total to the selective extinction. It is assumed that the core of the two-layer grains consists of ''astronomical silicate'' and the mantle of dirty ice and that they are completely or partly oriented under the influence of the Davis-Greenstein mechanism. A study is made of the dependence of R /sub V/ on the diameter of the grains and the degree and direction of their orientation. It is shown that to find the total extinction it is best to use the relation A /sub V/ = 1.1E(V - K), which holds to an accuracy less than or equal to 3% in a wide range of parameters of the problem.