We present the screening dependence theoretical investigations of the superconducting state parameters, i.e.electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature Tc, isotope effect exponent α, and effective interaction strength N0V of some CucZr100-C (C = 25, 30, 33, 35, 40, 45, 50, 55, 57,60 at.%) binary amorphous alloys by employing the well-known empty core model potential of Ashcroft. Five screening functions proposed by Hartree, Taylor, Ichimaru-Utsumi, Farid et al. and Sarkar et al. are used to study the screening influence on the aforesaid superconducting properties. The transition temperature Tc obtained from the Ichimaru-Utsumi screening function is found to be in excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with the other earlier reported data, which confirms the superconducting phase in the amorphous alloys.