Cyclic stresses due to passing wheels impose an accumulation of permanent strains in layers of unbound granular materials (UGMs) of flexible pavements. The hollow cylinder triaxial test would be the most appropriate test to simulate the in situ stress conditions but it is difficult to perform on UGMs due to their large maximum grain size. The simpler axisymmetric cyclic triaxial test does not consider the shear stress components. It can be performed with a constant confining pressure (CCP) or a variable confining pressure (VCP). CCP and VCP tests are commonly assumed to deliver similar residual and resilient strains as long as the average stress is the same. Thus, the simpler CCP test is mostly used in pavement engineering. However, this assumption is based on limited test data in the literature and may not be on the safe side. The present paper documents a comparative study of CCP and VCP tests on UGM. The study is mainly dedicated to the permanent deformations. The results show that only for some special stress paths do both types of tests deliver similar permanent axial or volumetric strains. For some other stress paths the CCP tests may underestimate the permanent axial strain in comparison to the corresponding VCP test.