A search for sidereal variations in the non-Newtonian force between two tungsten plates separated at millimeter ranges sets experimental limits on Lorentz invariance violation involving quadratic couplings of Riemann curvature. We show that the Loren
tz invariance violation force between two finite flat plates is dominated by the edge effects, which includes a suppression effect leading to lower limits than previous rough estimates. From this search, we determine the current best constraints of the Lorentz invariance violating coefficients at a level of $10^{-8}$ m$^{2}$.
