For coupled-channel resonance scattering we derive a model with a closed form solution for the T -matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method focuses on the expansion of the transition matrix elements, Γ(s), in known analytical functions. The appropriate hadronic form factors and the related energy shifts can be determined from the scattering data. The differences between this method and the K-matrix and the Breit-Wigner approximation are illustrated in the case of the S11 resonances S11(1535) and S11(1650).