In this talk, we will discuss the behavior of the Yamabe flow on an asymptotically flat (AF) manifold. We will first show that any AF manifold $(M^n, g_0)$ with the Yamabe flow existing on a time interval $[0, T]$ must satisfy a uniform $L^2$ Euclidean-type Sobolev inequality. This would allow us to control the $L^{n/2}$-norm of the scalar curvature along the Yamabe flow. After that, we will obtain the estimates on higher order integral norms of the scalar curvature, which will eventually lead to the long-time existence of the Yamabe flow starting from an AF manifold. We will also discuss the convergence along the Yamabe flow. This is joint work with Eric Chen.