Suspended Microchannel Resonators (SMRs) are hollow resonant structures containing an embedded U-shaped microfluidic channel. Theoretical and experimental results have proved that in these devices the energy dissipation is a non-monotonic function of the fluid viscosity (or Reynolds number), while in conventional cantilevers it always increases with the viscosity as the damping from the fluid on the solid structure increases. In this project, both a Mathematica code and a FEM model are produced to validate the theoretical and experimental results on the energy dissipation in these devices. To reduce the computational effort an eigenvalue study is performed. The incompressible and compressible cases are investigated while changing the fluid and device characteristics. Our numerical model works fine where the experimental data are provided but it is in contrast with the theoretical model at low Reynolds number (high viscosities). We consider it valid in the region of interest and send to further investigation the difference at low Reynolds number between theory and numerics.