Devon's bill rose from £2m in 2012/13 to £6.4m in 2014/15 and Plymouth's bill rose from £171,000 in 2012/13 to £824,000 in 2014/15.
The British Association of Social Workers, responding to figures obtained by the BBC, said use of agency workers had a detrimental effect on clients.
The Department of Health declined to comment.
Figures obtained by BBC Freedom of Information request.
Maris Stratulis from the British Association of Social Workers said: "Investment in retention of social workers, good supervision, workforce development and valuing the profession is essential rather than increasing spend on agency staff.
She added that relying on such workers, "often results in fragmentation of service delivery and a constant change of social workers for vulnerable children, families and adults".
Devon County Council said "Nationally there's a shortage of qualified children's social workers, so like most local authorities, Devon uses experienced agency social workers on temporary basis."
Plymouth City Council: "Nationally there is a shortage of social workers and in order to provide an essential service the use of agency staff is required.
"In order to resolve this matter we are working far more closely with universities to bring forward a new cohort of social workers and following proactive recruitment campaigns we are also now seeing an increase number of experienced social workers join us."
South West councils spent £16.5m on agency social workers last year, up from £6.8m in 2012, it has emerged.