ABSTRACT The Cherenkov Telescope Array (CTA) will be the next generation instrument for the very high energy gamma-ray astrophysics domain. With its enhanced sensitivity in comparison with the current facilities, CTA is expected to shed light on a varied population of sources. In particular, we will achieve a deeper knowledge of the Crab nebula and pulsar, which are the best characterized pulsar wind nebula and rotation powered pulsar, respectively. We aim at studying the capabilities of CTA regarding these objects through simulations, using the main tools currently in development for the CTA future data analysis: gammapy and ctools. We conclude that, even using conservative Instrument Response Functions, CTA will be able to resolve many uncertainties regarding the spectrum and morphology of the pulsar and its nebula. The large energy range covered by CTA will allow us to disentangle the nebula spectral shape among different hypotheses, corresponding to different underlying emitting mechanisms. In addition, resolving internal structures (smaller than ∼0.02° in size) in the nebula and unveiling their location, would provide crucial information about the propagation of particles in the magnetized medium. We used a theoretical asymmetric model to characterize the morphology of the nebula and we showed that if predictions of such morphology exist, for instance as a result of hydrodynamical or magneto-hydrodynamical simulations, it can be directly compared with CTA results. We also tested the capability of CTA to detect periodic radiation from the Crab pulsar obtaining a precise measurement of different light curves shapes.