Gas ows through micro lters are simulated in the continuum and slip ow regimes as a function of the Knudsen, Reynolds, and Mach numbers. The numerical simulations are based on the spectral element formulation of compressible Navier-Stokes equations, which utilize previously developed high-order velocity slip and temperature jump boundary conditions. Both slip and no-slip simulations are used to identify the rarefaction effects. The simulation results show skin friction and form-drag reduction with increased Knudsen number. Pressure drops across the lters are compared against several empirical scaling laws, available in the literature. Compressibility becomes important for high-speed ows, creating large density uctuations across the micro lter elements. For high-Machnumber ows interactions between thermal and kinetic energies of the uid are observed. It is also shown that viscous heating plays a signi cant role for high-speed gas ows, which impact heat-transfer characteristics of micro lters.