  In this paper, we consider periodic soft inclusions $T_{\epsilon}$ with
periodicity $\epsilon$, where the solution, $u_{\epsilon}$, satisfies
semi-linear elliptic equations of non-divergence in
$\Omega_{\epsilon}=\Omega\setminus \bar{T}_\epsilon$ with a Neumann data on
$\partial T^{\mathfrak a}$ . The difficulty lies in the non-divergence
structure of the operator where the standard energy method based on the
divergence theorem can not be applied. The main object is developing a
viscosity method to find the homogenized equation satisfied by the limit of
$u_{\epsilon}$, called as $u$, as $\epsilon$ approaches to zero. We introduce
the concept of a compatibility condition between the equation and the Neumann
condition on the boundary for the existence of uniformly bounded periodic first
correctors. The concept of second corrector has been developed to show the
limit, $u$, is the viscosity solution of a homogenized equation.
