Mass attenuation coefficients ($\mu/\rho$) for Zr, Nb, Mo and Pd elements around their $K$-edges are measured at 14 energies in the range 15.744–28.564 keV using secondary excitation from thin Zr, Nb, Mo, Rh, Pd, Cd and Sn foils. The measurements were carried out at the $K_{\alpha} and $K_{\beta}$ energy values of the target elements by two techniques: (1) Proton-induced X-ray emission (PIXE) and (2) $^{241}$Am (300 mCi) source. In PIXE, 2 MeV proton-excited X-rays were detected by a Si(Li) detector. In the second case, X-rays excited by 59.54 keV photons from the targets were counted by an HPGe detector under a narrow beam good geometry set-up with sufficient shielding. The results are consistent with theoretical values derived from the XCOM package and indicate that the PIXE data have better statistical accuracy.