We present electron and photon ionization cross sections for the BeH molecule. A configuration-average distorted-wave method is used to compute the electron and photon ionization cross sections based on earlier molecular structure tabulations. The electron ionization cross sections are compared with previous Deutsch-Mark and binary encounter Bethe calculations. Total single ionization cross sections are found to be larger due to the inclusion of an inner subshell. The photon ionization cross sections are compared with previous molecular-adapted quantum defect orbital calculations. The total single ionization cross sections are again found to be larger due to the inclusion of an inner subshell. We also calculated electron and photon ionization cross sections for a low lying excited configuration of BeH.