Jack Mount is accused of committing the offences in Birmingham, Shropshire and Yorkshire between 1954 and 1979.
The 95-year-old is the former head of privately-run Brookside School near Craven Arms in Shropshire.
Mr Mount, from Paradise Lawn in South Molton, Devon, has Parkinson's disease. He denies the allegations and is due to formally enter a plea in January.
The charges consist of nine counts of rape, six of gross indecency, nine of indecent assault and eight allegations of other sexual offences.
He is alleged to have committed the offences against six girls and six boys.
One offence was allegedly committed in Barnsley and then West Riding in the mid-1950s. Three are said to have occurred in Birmingham between 1957 and 1962.
The remaining 28 charges relate to allegations of sexual abuse against boys and girls in south Shropshire between 1967 and 1979.
Mr Mount appeared at both Birmingham Magistrates' Court and Birmingham Crown Court earlier. He was granted unconditional bail.
A former head teacher has appeared in court accused of 32 sex attacks against 12 children.