The low-lying energy levels, [Formula: see text] transition probabilities and [Formula: see text]-factors of even–even medium-mass tellurium isotopes have been studied by employing the projected shell model (PSM) approach. The oblate ground state deformations are taken in this study that were predicted in previous relativistic Hartree Bogoliubov mean field study. The low-lying yrast and yrare states are reproduced well in these calculations. The energy and configuration of yre states are also predicted. The experimental [Formula: see text] values and their systematics with neutron number are reproduced well in the medium-mass Te isotopes. The experimental data are available for [Formula: see text]-factors of 2[Formula: see text] states of [Formula: see text]Te isotopes which is in line with these calculations. The enhancement of [Formula: see text]-factors at spin [Formula: see text] = 6[Formula: see text] in all the Te isotopes considered may be attributable to the alignment of protons in [Formula: see text] subshell. Furthermore, the reduction of [Formula: see text]-factors at spin [Formula: see text] in [Formula: see text]Te and [Formula: see text] in [Formula: see text]Te may be attributable to the alignment of neutrons in the [Formula: see text] subshell. The 8[Formula: see text] states of [Formula: see text]Te are envisaged to be of [Formula: see text] nature and in [Formula: see text]Te these states are found to be of [Formula: see text] nature.