Computer simulation results are presented for an atomistic pair potential model of 1,4-dioxane which takes into account molecular flexibility. The model has been conceived to be applied to the study of solvatochromism and solvation dynamics in the presence of the polar probe coumarin C153. Computer simulations on the pure liquid have produced thermodynamical, structural, and dynamical data in good agreement with available experimental measures. This constitutes a valuable test of the 1,4-dioxane all-atom model employed. The study of solute-solvent interactions for C153 in 1,4-dioxane has been motivated by the aim of casting light, through simulations, on the interesting experimental findings according to which such a solvent behaves as a "polar" solvent with respect to dynamic solvation properties. Molecular dynamics is particularly suitable to model the process and provides an interpretation of the so-called "dioxane anomaly". An investigation of the structure of the solvation shell and of the dynamics of solvation is presented and discussed. In particular, the satisfactory accordance between simulated and experimental solvation response implies that the simulations give a reliable description of both solute and solvent at a molecular level and reinforces the idea that the explicit inclusion of discrete solvent molecules is needed for a realistic treatment of solvation phenomena in which the local structure of the liquid plays a key role.