Molecular dynamics studies of liquids consisting of either 1,4-dioxane or 1,3-dioxane molecules are performed with the aim to understand why and how liquid 1,4-dioxane may act as a polar solvent in solute-solvent interactions, despite the lack of a permanent dipole moment of the solvent molecules. An intermolecular pair potential is designed such that static quantities as density and radial distribution function, as well as dynamic quantities as diffusion coefficient and rotation correlation functions, are correctly recovered from the simulations, both for liquid 1,4-dioxane and for liquid 1,3-dioxane. An additional test is the comparison of the dielectric constant of liquid 1,3-dioxane from experiment (epsilon(exp) = 13.6) with the value derived from the MD simulated reaction field and liquid density (epsilon(calc) = 12.8). In these simulations, a 1,3-dioxane molecule is selected as a dipolar probe, whose dipole moment (mu(probe)) is then changed artificially by varying its site charges. The reaction field F at the center of the dipolar probe, arising from orientation polarization of the solvent molecules, is calculated. This yields the dielectric constant by applying Onsager＇s expression for the reaction field. When the dipolar 1,3-dioxane is embedded in liquid 1,4-dioxane, a simulated field F is obtained, whose magnitude is of the same order of magnitude as Onsager＇s reaction field in polar organic solvents. In both liquids the simulated field F arises nearly entirely from the local dipoles of the solvent molecules encountered in the first shell around the dipolar probe. An effective dielectric constant of liquid 1,4-dioxane of about 7 is obtained, which may be used to calculate solvatochromic shifts of dipolar solutes in this solvent on the basis of Onsager＇s reaction field, provided that no specific solute solvent interactions are involved.