In the `90s, Phong and Stein established sharp estimates for oscillatory operators with real analytic phase. In this talk, we present a trilinear extension of their work. The study is motivated by the work of Christ, Li, Tao and Thiele considering decay estimates for certain multilinear oscillatory integrals. The proof the sharp estimates relies on a self-contained algorithm of two-variable resolution of singularities, which may be of independent interest.