The R-matrix method is used to calculate the elastic and the excitation cross sections from the ground state X (2) Pi to the four electronically excited states A (2)Sigma(+), 1 (4)Sigma(-), 1 (2)Sigma - and 1 (2) Delta the SH radical. Configuration interaction (CI) wavefunctions are used to represent the target states. In our target CI model, we keep 1sigma, 2sigma, 3sigma and 1pi orbitals fully occupied and the remaining seven valence electrons are free to occupy 4sigma, 5sigma, 6sigma, 2pi and 3pi molecular orbitals. This model gives an equilibrium bond length, R-e, of the X (2) Pi state equal to 2.568 a(0) which is in good agreement with the experimental value 2.535 a(0) and a SH equilibrium dipole moment of 0.795 D which is close to the experimental value of 0.758 D. Scattering calculations are performed in the static-exchange, the static-exchange plus polarization and the 5-state models. The vertical excitation energies lie in the range 4.01-7.42 eV. We find a bound state of SH- of (1) Sigma(+) symmetry with an electron affinity of 1.37 eV at R-e for the 5-state model. We also find two shape resonances in (1) Pi symmetry and (3) Pi symmetry with a common configuration 2pi(3)6sigma, and two core-excited shape resonances of (1)Sigma(+) and (3)Sigma(+) symmetries with A (2) Sigma(+) as the parent state. Born correction is applied for dipole allowed transitions to account for higher partial waves excluded in the R-matrix calculation. Cross sections are given for scattering energies up to 10 eV.