The union claims the council and director of human resources George Farquhar persistently refused to investigate specific complaints about work-related stress suffered by staff in the human resources department.
Eight HR employees claim to have suffered 'bullying, indifference and vindictiveness by senior staff', said Unison's senior regional manager Jim Waller.
Mr Waller said the union had carried out the survey of HR staff after Mr Farquhar 'refused point-blank' to investigate the reasons for high levels of sickness absence, ill-health retirements and stress in his department.
He referred to a backdrop of financial cuts and reorganisation and said the council had introduced 'a whole range of policies to support employees in the workplace'.
These included commissioning the Institute of Occupational Medicine in October to conduct an independent audit of workplace stress.