The goal of the present work is to study theoretically the structure of water inside the water cylinder of the inverse hexagonal mesophase (HII) of glyceryl monooleate (monoolein, GMO), using the method of molecular dynamics. To simplify the computational model, a fixed structure of the GMOtube is maintained. The non-standard cylindrical geometry of the system required the development and application of a novel method for obtaining the starting distribution of water molecules. A predictor-corrector schema is employed for generation of the initial density of water. Molecular dynamics calculations are performed at constant volume and temperature (NVT ensemble) with 1D periodic boundary conditions applied. During the simulations the lipid structure is kept fixed, while the dynamics of water is unrestrained. Distribution of hydrogen bonds and density as well as radial distribution of water molecules across the water cylinder show the presence of water structure deep in the cylinder (about 6 Å below the GMO heads). The obtained results may help understanding the role of water structure in the processes of insertion of external molecules inside the GMO/water system. The present work has a semi-quantitative character and it should be considered as the initial stage of more comprehensive future theoretical studies.