Coupled-channels optical model code OPTMAN is used as an alternative to experimental approach to evaluate the total reaction cross section for four different isotopes of Neptunium, Plutonium, Americium and Curium as examples of heavy rotational nuclei of the transuranium elements over energy range of 10 to 20 MeV. The choice of the selected isotopes is as a result of their importance in the modern day nuclear reactor and the energy range 10-20 MeV is the energy range of neutron produced in neutron generators and the maximum energy possessed by neutrons which are born in fission reaction. Results from the total reaction cross section calculations show that the percentage deviation of total cross section from Evaluated Nuclear Data File, ENDF, values obtained is less than 1 % for Np-237, Pu-238, Am-243, and Cm-244 at energies greater or equal to 14 MeV for Np-237, 16 MeV for Pu-238 and Am-243 and 18 MeV for Cm-244. The nucleus of transuranium isotopes are symmetric and the activities of rotation and vibrations (beta - quadrupole, octupole vibrations and Gamma - quadrupole vibrations) cannot be ignored.