Thermal design of MEMS/NEMS packages is drawing more attention from both industrial and academic communities. When the system becomes extremely small, the atomistic effects have to be taken into account correctly. The finite element method is not capable of accurately capturing all the information, especially when it is applied to the small dimensions. In order to study failure behavior, precise modeling of interfacial thermal conductance is essential. In this paper, a multi-scale model is proposed to research interfacial thermal resistance in MEMS/NEMS packaging. The model combines a molecular dynamics simulation for the critical regions within the system with a FE method for a continuum description of the remainder of the system. For non-equilibrium simulations, the establishment of the proper boundary condition is very difficult. In this coupled model, the continuum subdomain serves primarily as a boundary model that provides the low frequency impedance and a sink for the energy associated with outgoing waves of the molecular dynamics model. The simulations results show that the temperature distribution is non-uniform along the interface, and the interface tends to accumulate much heat when the temperature of heat source changed. At the primary stage, the interfacial thermal resistance is unstable and will become very large at certain time steps. At the last stage, the change of interfacial thermal resistance tends to be stable. There are few direct experimental measurements of the interfacial thermal resistance between dissimilar materials, while the similar experimental results support the conclusions in this paper.