The behavior of confined fluids is of great interest due to the proliferation and applications of micro- and nanofluidic devices. Recent computational and experimental results have shown that fluids exhibit unusual phase change behavior when confined to very small length scales where the fluid physics is dominated by interactions with the confining channel walls. In particular, understanding the liquid-vapor phase transition and bubble nucleation process in confined spaces presents opportunities for making valves and pumps in nanofluidic networks. In this paper, we present molecular dynamics simulations of thermal bubble nucleation in fluids confined in nanochannels. To verify the computational models, bulk argon and bulk water were first modeled under conditions similar to those reported in the literature. The results were similar to those presented in the literature, indicating that our computational models could reproduce published data. We then modeled argon and water systems confined between two parallel silicon plates with nanometer separation. To simulate cases more extensively encountered in reality, we performed Molecular Dynamics (MD) simulations in the isothermal-isobaric (NPT) ensemble by allowing the top silicon plate to move up and down under a constant external pressure during the simulation. For either the nano-confined argon or the nano-confined water system, results indicated no bubble generation under an external pressure of 0.1 MPa, even for temperatures much higher than the boiling temperature of the respective fluids at 0.1 MPa. We also observed that there was no bubble generation in either the argon or water NPT system when the external pressure was reduced to as low as 0.01 MPa. The density of the nano-confined fluids at constant temperature was observed to be independent of external pressure on the system. This suggests that the nanoconfined fluids behave like liquids with low compressibility even at temperatures close to their superheat limit.