We test the relativistic precession model (RPM) and the MHD Alfvén wave oscillation model (AWOM) for the kHz QPOs by the sources with measured NS masses and twin kHz QPO frequencies. For RPM, the derived NS mass of Cyg X-2 (SAX J1808.4-3658 and 4U 1820-30) is 1.96 ± 0.10 M ⊙ (2.83 ± 0.04 M ⊙ and 1.85 ± 0.02 M ⊙ ), which is ∼ 30% (100% and 40%) higher than the measured result 1.5 ± 0.3 M ⊙ (< 1.4 M ⊙ and 1.29 +0.19 −0.07 M ⊙ ). For AWOM, where the free parameter of model is the density of star, we infer the NS radii to be around 10 ∼ 20 km for the above three sources, based on which we can infer the matter compositions inside NSs with the help of the equations of state (EOSs). In particular, for SAX J1808.4-3658, AWOM shows a lower mass density of its NS than those of the other known kHz QPO sources, with the radius range of 17 − 20 km, which excludes the strange quark matter inside its star.