The equilibrium structure and potential energy surface of calcium dihydride, CaH2, have been determined from large-scale ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with basis sets of quadruple- and quintuple-ζ quality. The CaH2 molecule was found to be quasilinear. The HCaH bending potential function was predicted to be extraordinarily flat near the minimum, located at the HCaH angle of 164°. The barrier to linearity was calculated to be just 6 cm(-1). The vibrational-rotational energy levels of various isotopomers were predicted using the variational method. The calculated vibrational fundamental frequencies are in good agreement with the results of matrix-isolation studies, and the other predicted spectroscopic constants can assist in the future detection of calcium dihydride in the gas phase.