In this paper, electromagnetic scattering by general bi-isotropic objects is investigated on the basis of the surface integral equations. By applying the surface equivalent principle, electromagnetic fields inside a homogeneous bi-isotropic region can be represented in terms of equivalent electric and magnetic currents distributed over its boundary surface. Upon imposing boundary conditions, a series of coupled surface integral equations is obtained. These equations are then solved numerically by the application of the method of moments combined with the Galerkin technique. In specific implementation, the triangulated patches are used to approximate the surface of the arbitrarily shaped bi-isotropic object, and the Rao-Wilton-Gllison function is selected as the basis function and testing function. The developed formulations are generalized and are capable of treating Tellegen and Pasteur media. To validate the theoretical formulations, numerical results for Pasteur objects are provided to compare with the available data, and good agreements are observed. Furthermore, the scattering characteristics of Tellegen objects are reported. The effects of bi-isotropic parameters on the bistatic cross section are studied and discussed.