Numerical and simulation studies are done to determine deflection behavior of epitaxially deposited polysilicon encapsulation. Polysilicon encapsulation, which is used as physical protection for moving parts of MEMS devices, is applied with external pressure to replicate packaging processes. Polysilicon encapsulations of thickness 10, 20, 30, and 40 micron with seal oxide of thickness 2, 4, 6, 8, and 10 micron are analyzed. Ritz's and energy methods are used to numerically approximate surface deflection of polysilicon encapsulation when perpendicularly loaded with a uniform pressure varying from 10 to 100 atm. Simulation was done using CoventorWare ver.2001.3 software. It is observed that numerical analysis values approximate theoretical values for small deflection (W<t). Thus, numerical analysis could be use to predict deflection behavior of encapsulation in that region.