This paper proposes a time-domain volume integral equation based method for analyzing the transient scattering from a two-dimensional inhomogeneous cylinder by invoking the volume equivalence principle for both the transverse magnetic and electric cases. The cylinder is discretized into triangular cells, and the electric flux is chosen as the unknown. For the transverse magnetic case, the electric flux is defined on the surfaces of the triangles. For the transverse electric case, because of the electric charges induced inside and on the surface of the cylinder, the electric flux is defined on the edges of the triangles, and expanded in space in terms of two-dimensional surface roof-top basis functions. The time-domain volume integral equation is solved by using a marching-on-in-time scheme. Numerical results obtained using this method are in excellent agreement with the data obtained using the finite-difference time-domain method.