Orbital integrals appear on the geometric side of the trace formula, which is an important tool in the Langlands program. Explicit values or estimates of orbital integrals are rarely known, yet they are expected to be used to obtain information about automorphic representations via the trace formula. In joint work with S. Cho and Y. Lee, we establish lower bounds of the stable orbital integrals for the general linear group, the unitary group, and the symplectic group. Our approach involves assigning a stratification and applying smoothening.