Understanding the role of TiO2 in BaO-TiO2-SiO2 (BTS) glasses is one of the keys to develop new glasses and glass-ceramics for different technological applications. For the first time, molecular dynamics simulations were conducted to get new insights into the atomic structure of the BTS glasses and their elastic moduli. Various compositions are studied where SiO2 have been replaced by TiO2. The calculated mechanical properties of our models are observed to depend linearly on TiO2 content. However, the structure-induced changes are far from such dependence. The structural results indicate that BTS glasses are mainly built on four types of basic units: SiO4, TiO4, TiO5 and TiO6. This high structural heterogeneity induced by the three coordination states of Ti is found to have an impact on the medium range order by increasing the rings number, the polymerized regions, and by transforming Q(3)-Q(4) and Q(2) without neglecting the increase in Q(5) and Q(6) species. Those structural modifications of the BTS glass network features have been found to be consistent with available experimental data.