Elastic- and inelastic-neutron-scattering cross sections of elemental Hf, Gd, and Sm were measured at incident neutron energies of 0.3 to 1.5 MeV. The experimental resolution was sufficient to reasonably resolve elastic and inelastic processes and define individual inelastic cross sections for the most appreciably excited states. The total neutron cross sections were determined up to 1.5 MeV with resolutions of ≳2.5 keV. Within the precisions of the measurements all observed cross sections were relatively smooth functions of energy. The experimental results were compared with those obtained from calculations based upon both spherical and deformed optical potentials and statistical theory inclusive of fluctuation corrections. The calculated results were descriptive of measured total, elastic scattering and, to a lesser extent, inelastic scattering cross sections. Experimental and calculated results were compared with previously reported measured values and with the contents of several evaluated neutron-data sets employed in reactor design.