The astrophysical importance of the SiH radical has motivated significant experimental and theoretical work. However, only the X (2)Pi and A (2)Delta states of SiH have been extensively investigated experimentally, while the study of higher excited states is rather limited. From a theoretical point of view, most of the studies have been focused on spectroscopic and thermochemical quantities of the ground state. The lack of accurate spectroscopic parameters (r(e),D-e,omega(e),omega(e)x(e),alpha(e),(D) over bar (e),T-e) pertaining to higher excited states was the driving force of the present work, in line with our previous study of the isovalent CH molecule [A. Kalemos, A. Mavridis, and A. Metropoulos, J. Chem. Phys. 111, 9536 (1999)]. Using the multireference configuration interaction approach coupled with very large correlation-consistent basis sets, we have constructed potential energy curves for 18 molecular states correlating to Si(P-3,D-1,S-1,S-5,P-3,P-1)+H(S-2). At the same level, the potential energy curve of the ground SiH+ state (X (1)Sigma(+)) has also been constructed. We report total energies, dissociation energies, and the usual spectroscopic constants for Si-28-H-1,H-2 and for all states studied. Most of our results are in excellent agreement with existing experimental values. In particular, we believe that our dissociation energy for the X state, D-e=73.28 kcal/mol, is the most reliable reported so far in the literature.