The aim of this computational study is to accurately predict complicated flowfields and obtain accurate aerodynamic forces of a thin folding plate under low Reynolds number range. The thin folding plate is a bent flat plate at a point, and is known to cause the non-linear lift curve at the flow regime. One of Cartesian-Mesh CFD solvers, Building-Cube Method (BCM), is used to compute the flows around the thin airfoils. The computed results of a thin flat plate and a thin folding plate are compared with the experimental results. Throughout this study, the effectiveness of BCM against thin airfoils at low Reynolds number flows is discussed. It is expected that the rapid increase of negative pressure in separation bubble at leading-edge causes the increase of Cl, which leads the non-linear lift curve.