An ab initio configuration interaction (CI) study including the spin-orbit interaction is carried out for numerous valence and Rydberg states of the SbH radical by employing a relativistic effective core potential for the antimony atom. The computed spectroscopic constants are in good agreement with available experimental data, with a tendency toward a slight overestimation of bond lengths (by 0.01-0.03 Angstrom) and T-e values (by 370-550 cm(-1)) for the lowest singlet states. Measured excitation energies and spin-orbit splittings for the A (3) Pi multiplet are also accurately reproduced in the present calculations and the Omega=0(-), 1, and 2 components of this state are shown to be strongly predissociated due to spin-orbit interaction with the corresponding components of the repulsive (5) Sigma(-) state. The most stable representative of the A (3) Pi multiplet, A(4)O(+), is found to possess a very unusual potential curve with a double minimum and a fairly low barrier to dissociation. Based on a vibrational analysis of this state it is concluded that the earlier observed BO+ and CO+ electronic states should be attributed to the v=O and 2 vibrational levels of the A(4)0(+) state, while the state experimentally assigned as A (3) Pi(0+) corresponds to the A(4)0(+), v=1 level. Dipole moments mu(v =0) for the ...sigma(2) pi(2) X-3 Sigma(-), a (1) Delta and b (1) Sigma(+) states are computed to have small (e.g., -0.238 D for X-1 (3) Sigma(0+)(-)) and nearly equal negative values (Sb+H- polarity). The dipole transition moments and the corresponding radiative lifetimes for a number of low-energy electronic transitions have also been computed. Many other bound states and avoided crossings are indicated in the calculations which may be of relevance in future experimental studies of this system.