To understand the importance of Y-base adjacent to the anticodon stabilizing codon-anticodon interaction, a study has been undertaken for the model compound involving the interaction between Y-base and anticodon as well as the participation of water molecule by calculating the conformational free energy using an empirical potential function. We restrict our analysis to sites directly associated with Y-base by varying only the backbone torsion angles of Y-base. The hydration and $Mg^{+2}$ binding effects on the conformational stability of Y-base are calculated and discussed. The free Y-base is proved to be less stable than the hydrated one. The free energy change due to the hydration of Y-base amounts to -119.5 kcal/mole, in which the conformational energy change is -142.4 kcal/mole and the configurational entropy change is -76.9 e. u. It is found that the water molecules bound to Y-base and $Mg^{+2}$ contribute to the conformation of Y-base dominantly.