A time-domain method is presented for analyzing arbitrarily shaped thin resistive sheets (TRSs). The method makes use of the surface impedance matrix and piecewise linear recursive convolution techniques. The extracted data of pole-residue pairs, which are not dependent on the geometry and material of the TRSs, are given. The stability condition for the finite-difference time-domain (FDTD) simulation of the TRSs is provided for the first time. This method has been combined with a conformal scheme to analyze arbitrarily shaped TRSs. The simulation results for three test cases are given to show the accuracy and stability of the proposed method.