Cepheids are pulsating variable stars with a periodic chromospheric response at UV wavelengths close to their minimum radius phase. Recently, an X-ray variable signature was captured in observations during the emph{maximum} radius phase. This X-ray emission came as a surprise and is not understood. In this work, we use the modern astrophysical code, PLUTO, to investigate the effects of pulsations on Cepheid X-ray emission. We run a number of hydrodynamic numerical simulations with a variety of initial and boundary conditions in order to explore the capability of shocks to produce the observed phase-dependent X-ray behavior. Finally we use the Simulated Observations of X-ray Sources (SOXS) package to create synthetic spectra for each simulation case and link our simulations to observables. We show that, for certain conditions, we can reproduce observed X-ray fluxes at phases 0.4--0.8 when the Cepheid is at maximum radius. Our results span a wide range of mass-loss rates, $2times10^{-13}$--$3times10^{-8}$ $M_odot$ yr$^{-1}$, and peak X-ray luminosities, $5times10^{-17}$--$1.4times10^{-12}$ erg cm$^{-2}$ s$^{-1}$. We conclude that Cepheids exhibit textit{two component emission} with (a) shock waves being responsible for the phase dependent variable emission (phases 0.2 - 0.6), and (b) a separate quiescent mechanism being the dominant emission mechanism for the remaining phases.
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