The cross sections of 89Y(n, 3n)87m,87gY and 209Bi(n, 4n)206Bi reactions at a neutron energy of 30 MeV are measured by making use of neutron beams of continuous energy spectra and a subtraction method. By impinging proton beams of 30 and 35 MeV to a thick beryllium target, neutron beams of continuous and broad energy spectra are produced and are guided to Y and Bi sample targets. The difference between the two neutron spectra generated by two neighboring proton energies is found to be peaked in a narrow energy range and thus can be regarded as quasi-monoenergetic, which can be used to extract (n, xn) cross sections. The uncertainty in the neutron fluence is reduced by analyzing the activities of aluminum and niobium reference samples placed on top of the Y and Bi samples. The use of a subtraction method by employing neutron beams of continuous energy spectra gives us the 89Y(n, 3n)87m,87gY and 209Bi(n, 4n)206Bi cross sections in fair agreement with the existing experimental data and nuclear data libraries.