The Educational Institute of Scotland (EIS) found that individual local authorities are paying almost £120,000 a year on the assessments.
They argue the tests have no academic value and are not necessary in terms of measuring pupils' achievements.
But the local authorities which use them insist they are a helpful way of providing information to parents about how their children are doing in reading and maths, and are useful in terms of identifying pupils who are struggling.
Standardised baseline assessments are sat by pupils every two years in some primary schools, as well as in the early years of secondary school. Pupils sit tests in maths and literacy.
Twenty six of Scotland's 32 local authorities responded to a freedom of information request from the EIS, which found that while some councils had no money allocated to the assessments, one council set aside up to £120,000 year.
Larry Flanagan, EIS general secretary, said: "The EIS has serious concerns over the large sums of money being spent on standardised baseline assessment in our schools. While some local authorities claim to be spending nothing on these tests or - more accurately - allocate no specific budget to schools to pay for them, other authorities are allocating very large sums of money, up to £120,000 in one case, to put pupils through these tests.
"The EIS is very clear that standardised baseline assessment offers little or no educational value and is not a necessary part of measuring pupils' achievement."
Schools in East Renfrewshire and Aberdeenshire are among those that use the tests. In the former area, which has some of the highest-performing schools, the tests are carried out in primary one, three, five and seven as well as in the second year at secondary school.
On its website East Renfrewshire council says the tests give teachers and parents a fuller picture of what children are attaining in school, provide a profile of every pupil in terms of literacy and numeracy and identify areas of weakness.
Aberdeenshire Council said on its website that the tests are valuable in improving learning and teaching. It added the tests help consolidate what a child is learning and show how different groups of pupils are doing.